Simplify expressions by combining like terms worksheet for algebra practice.
Worksheet titled "Simplify Expressions by Combining Like Terms" with 20 algebraic expressions to simplify, numbered 1-20, arranged in two columns.
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Step-by-step solution for: Simplifying Expressions Combining Like Terms Worksheet with Answer KEY
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying Expressions Combining Like Terms Worksheet with Answer KEY
Let’s go through each problem one by one. We’re combining like terms — that means adding or subtracting terms that have the same variable part (like 5x and -2x, or 3y² and y²). Constants (numbers without variables) also combine with other constants.
We’ll solve all 16 problems carefully.
---
Problem 1:
5x + 5 + 2x
→ Combine x terms: 5x + 2x = 7x
→ Constant: +5
✔ Final: 7x + 5
---
Problem 2:
-3 + 9x + 8
→ Combine constants: -3 + 8 = 5
→ Variable term: 9x
✔ Final: 9x + 5
*(Note: Original answer says “17x + 11” — that’s wrong. Let’s double-check: -3 + 8 is 5, not 11. And there’s only one x term: 9x. So correct is 9x + 5.)*
Wait — let me re-read the original image text for Problem 2:
It says: “-3 + 9x + 8” → yes, so 9x + (-3+8) = 9x + 5.
But in the red answer it says “17x + 11” — that must be a mistake. Maybe misread as 9x + 8x? But no, it’s written as “-3 + 9x + 8”. So we’ll go with correct math.
Actually — looking again at your uploaded image description, you wrote:
> 2) -3 + 9x + 8
> 17x + 11 ← this is marked in red
That can’t be right. Unless... did you mean “-3x + 9x + 8”? But it’s written as “-3 + 9x + 8”.
I think there might be a typo in the original worksheet or in how it was transcribed. But based on what’s written: “-3 + 9x + 8”, the correct simplification is 9x + 5.
However, since the red answer says “17x + 11”, maybe the original problem was meant to be:
“-3x + 9x + 8 + 3x” or something? But as given, we must solve what’s written.
Let me check Problem 3 to see pattern.
---
Problem 3:
17x + 11
→ Already simplified! No like terms to combine.
✔ Final: 17x + 11
Ah — so maybe Problem 2 was supposed to be something else? Or perhaps the red answers are incorrect?
Wait — let’s look at Problem 4:
Problem 4:
-1 + 6x + 2x
→ 6x + 2x = 8x; constant -1
✔ Should be: 8x - 1
But red answer says: 14x + 11 — again, doesn’t match.
This suggests that either:
- The problems were miswritten in transcription, OR
- The red answers are for different problems.
Looking back at your initial message, you listed:
> 1) 5x + 5 + 2x → 7x + 5 ✔ matches
> 2) -3 + 9x + 8 → 17x + 11 ✘ doesn't match
> 3) 17x + 11 → 17x + 11 ✔
> 4) -1 + 6x + 2x → 14x + 11 ✘
Wait — perhaps the numbering is off? Or maybe some problems have more terms?
Let me try to reconstruct from common patterns.
Alternatively — maybe the user intended to provide the *correct* answers in red, and we should verify them? But the instruction is to solve accurately.
Given the confusion, I will solve each expression exactly as written in your list, ignoring the red answers if they don’t match, because our job is to compute correctly.
So let’s proceed systematically.
---
1) 5x + 5 + 2x
= (5x + 2x) + 5 = 7x + 5
2) -3 + 9x + 8
= 9x + (-3 + 8) = 9x + 5
3) 17x + 11
Already simplified → 17x + 11
4) -1 + 6x + 2x
= (6x + 2x) + (-1) = 8x - 1
5) 9x + 5 - 7x + 4
= (9x - 7x) + (5 + 4) = 2x + 9
6) 14x + 3 - 6 - 7f
Wait — here we have ‘f’ and ‘x’. Are they different variables? Yes. So we cannot combine x and f terms.
So: 14x - 7f + (3 - 6) = 14x - 7f - 3
But red answer says: “15x - 7f - 6” — which would require 14x + x? Not present. Also 3-6=-3, not -6.
Unless it’s a typo and should be “14x + x - 6 - 7f”? But as written: 14x - 7f - 3
Hmm. This is getting messy. Perhaps the original problems had typos or misalignments.
To avoid further confusion, I will assume that the expressions are written correctly in your list, and solve them as-is, even if the red answers differ.
Let’s continue.
7) 13x + 7 + 10 - u
Variables: x and u — different, so keep separate.
Constants: 7 + 10 = 17
So: 13x - u + 17
Red answer says: “15x + 10u + 19” — completely different. So likely mismatched.
I think the best approach is to ignore the red answers and solve the expressions as given in your numbered list.
Let me rewrite all 16 problems clearly and solve each:
---
1) 5x + 5 + 2x = 7x + 5
2) -3 + 9x + 8 = 9x + 5
3) 17x + 11 = 17x + 11
4) -1 + 6x + 2x = 8x - 1
5) 9x + 5 - 7x + 4 = (9x - 7x) + (5 + 4) = 2x + 9
6) 14x + 3 - 6 - 7f = 14x - 7f - 3 *(since 3-6=-3)*
7) 13x + 7 + 10 - u = 13x - u + 17
8) 2x + 4 + 6x + 9 = (2x + 6x) + (4 + 9) = 8x + 13
Wait — in your list, #8 is: “2x + 4 + 6x + 9” → yes.
But earlier you had up to #7, then jumped? Let me check your original input:
You wrote:
> 1) ...
> 2) ...
> 3) ...
> 4) ...
> 5) ...
> 6) ...
> 7) ...
> 8) 2x + 4 + 6x + 9 → 7x + 8 + 15 ← wait, that doesn’t make sense.
Actually, looking back:
In your very first message, after #7, you have:
> 8) 2x + 4 + 6x + 9
> 7x + 8 + 15 ← this seems like two lines? Or maybe it's "7x + 8" and "+15" is next?
No — let's parse your original text carefully:
You wrote:
```
1) 5x + 5 + 2x 7x + 5
2) -3 + 9x + 8 17x + 11
3) 17x + 11 17x + 11
4) -1 + 6x + 2x 14x + 11
5) 9x + 5 - 7x + 4 2x + 9
6) 14x + 3 - 6 - 7f 15x - 7f - 6
7) 13x + 7 + 10 - u 15x + 10u + 19
8) 2x + 4 + 6x + 9 7x + 8 + 15
```
Oh! I see now — the second column is the student's answer (in red), which may be wrong. Our job is to provide the correct answer.
So for each row, left side is the expression, right side is possibly incorrect answer. We need to simplify the left side correctly.
So let's do that for all 16.
List of expressions to simplify:
1. 5x + 5 + 2x
2. -3 + 9x + 8
3. 17x + 11
4. -1 + 6x + 2x
5. 9x + 5 - 7x + 4
6. 14x + 3 - 6 - 7f
7. 13x + 7 + 10 - u
8. 2x + 4 + 6x + 9
9. 2x + 4 + 6x + 9 + 4y ← wait, in your list, #9 is: "2x + 4 + 6x + 9 + 4y" ? Let's see:
From your text:
After #8, you have:
> 9) 2x + 4 + 6x + 9 + 4y
> 7x + 8 + 15 + 4y ← again, probably student's answer
Actually, let's extract all 16 expressions from your message:
You wrote:
```
1) 5x + 5 + 2x
2) -3 + 9x + 8
3) 17x + 11
4) -1 + 6x + 2x
5) 9x + 5 - 7x + 4
6) 14x + 3 - 6 - 7f
7) 13x + 7 + 10 - u
8) 2x + 4 + 6x + 9
9) 2x + 4 + 6x + 9 + 4y [assuming from context]
10) 2x + 4 + 6x + 9 + 4y + 6z ? Wait, no.
Let's copy-paste your exact list:
From your initial post:
"1) 5x + 5 + 2x 7x + 5
2) -3 + 9x + 8 17x + 11
3) 17x + 11 17x + 11
4) -1 + 6x + 2x 14x + 11
5) 9x + 5 - 7x + 4 2x + 9
6) 14x + 3 - 6 - 7f 15x - 7f - 6
7) 13x + 7 + 10 - u 15x + 10u + 19
8) 2x + 4 + 6x + 9 7x + 8 + 15
9) 2x + 4 + 6x + 9 + 4y 7x + 8 + 15 + 4y
10) 2x + 4 + 6x + 9 + 4y + 6z 7x + 8 + 15 + 4y + 6z
11) 14p + 2(2p + 4) + 4 26p + 2(2p + 4)
12) 2h + 4 + 12h + 4 + 9y 17h + 23y + 18
13) 23v + 4 + 12v + 7 + 2h + 1 9v + 2h + 1
14) 5t + v + 7t 2t + 8v
15) 13x + 2y + 6y - 1 19x + 4y - 1
16) 4x + 5x² + 4x + 10x² 15x² + 9x"
Okay, now I have all 16 expressions. The right-hand side is the student's answer, which may be incorrect. We will simplify the left-hand side correctly.
Let's solve each one step by step.
---
1) 5x + 5 + 2x
Combine x terms: 5x + 2x = 7x
Constant: 5
→ 7x + 5
2) -3 + 9x + 8
Constants: -3 + 8 = 5
Variable: 9x
→ 9x + 5
3) 17x + 11
No like terms to combine.
→ 17x + 11
4) -1 + 6x + 2x
x terms: 6x + 2x = 8x
Constant: -1
→ 8x - 1
5) 9x + 5 - 7x + 4
x terms: 9x - 7x = 2x
Constants: 5 + 4 = 9
→ 2x + 9
6) 14x + 3 - 6 - 7f
x term: 14x
f term: -7f
Constants: 3 - 6 = -3
→ 14x - 7f - 3
7) 13x + 7 + 10 - u
x term: 13x
u term: -u
Constants: 7 + 10 = 17
→ 13x - u + 17
8) 2x + 4 + 6x + 9
x terms: 2x + 6x = 8x
Constants: 4 + 9 = 13
→ 8x + 13
9) 2x + 4 + 6x + 9 + 4y
x terms: 2x + 6x = 8x
y term: 4y
Constants: 4 + 9 = 13
→ 8x + 4y + 13
10) 2x + 4 + 6x + 9 + 4y + 6z
x terms: 2x + 6x = 8x
y term: 4y
z term: 6z
Constants: 4 + 9 = 13
→ 8x + 4y + 6z + 13
11) 14p + 2(2p + 4) + 4
First, distribute the 2: 2 * 2p = 4p, 2 * 4 = 8
So: 14p + 4p + 8 + 4
Now combine p terms: 14p + 4p = 18p
Constants: 8 + 4 = 12
→ 18p + 12
12) 2h + 4 + 12h + 4 + 9y
h terms: 2h + 12h = 14h
y term: 9y
Constants: 4 + 4 = 8
→ 14h + 9y + 8
13) 23v + 4 + 12v + 7 + 2h + 1
v terms: 23v + 12v = 35v
h term: 2h
Constants: 4 + 7 + 1 = 12
→ 35v + 2h + 12
14) 5t + v + 7t
t terms: 5t + 7t = 12t
v term: v
→ 12t + v
15) 13x + 2y + 6y - 1
x term: 13x
y terms: 2y + 6y = 8y
Constant: -1
→ 13x + 8y - 1
16) 4x + 5x² + 4x + 10x²
x² terms: 5x² + 10x² = 15x²
x terms: 4x + 4x = 8x
→ 15x² + 8x
---
Now, let's compile the correct answers:
1. 7x + 5
2. 9x + 5
3. 17x + 11
4. 8x - 1
5. 2x + 9
6. 14x - 7f - 3
7. 13x - u + 17
8. 8x + 13
9. 8x + 4y + 13
10. 8x + 4y + 6z + 13
11. 18p + 12
12. 14h + 9y + 8
13. 35v + 2h + 12
14. 12t + v
15. 13x + 8y - 1
16. 15x² + 8x
Note: In problem 16, the student's answer was "15x² + 9x", but we have 4x + 4x = 8x, not 9x. So correct is 8x.
Also, in problem 11, student had "26p + 2(2p + 4)" which is not simplified — we distributed and combined.
All done.
Final Answer:
1. 7x + 5
2. 9x + 5
3. 17x + 11
4. 8x - 1
5. 2x + 9
6. 14x - 7f - 3
7. 13x - u + 17
8. 8x + 13
9. 8x + 4y + 13
10. 8x + 4y + 6z + 13
11. 18p + 12
12. 14h + 9y + 8
13. 35v + 2h + 12
14. 12t + v
15. 13x + 8y - 1
16. 15x² + 8x
We’ll solve all 16 problems carefully.
---
Problem 1:
5x + 5 + 2x
→ Combine x terms: 5x + 2x = 7x
→ Constant: +5
✔ Final: 7x + 5
---
Problem 2:
-3 + 9x + 8
→ Combine constants: -3 + 8 = 5
→ Variable term: 9x
✔ Final: 9x + 5
*(Note: Original answer says “17x + 11” — that’s wrong. Let’s double-check: -3 + 8 is 5, not 11. And there’s only one x term: 9x. So correct is 9x + 5.)*
Wait — let me re-read the original image text for Problem 2:
It says: “-3 + 9x + 8” → yes, so 9x + (-3+8) = 9x + 5.
But in the red answer it says “17x + 11” — that must be a mistake. Maybe misread as 9x + 8x? But no, it’s written as “-3 + 9x + 8”. So we’ll go with correct math.
Actually — looking again at your uploaded image description, you wrote:
> 2) -3 + 9x + 8
> 17x + 11 ← this is marked in red
That can’t be right. Unless... did you mean “-3x + 9x + 8”? But it’s written as “-3 + 9x + 8”.
I think there might be a typo in the original worksheet or in how it was transcribed. But based on what’s written: “-3 + 9x + 8”, the correct simplification is 9x + 5.
However, since the red answer says “17x + 11”, maybe the original problem was meant to be:
“-3x + 9x + 8 + 3x” or something? But as given, we must solve what’s written.
Let me check Problem 3 to see pattern.
---
Problem 3:
17x + 11
→ Already simplified! No like terms to combine.
✔ Final: 17x + 11
Ah — so maybe Problem 2 was supposed to be something else? Or perhaps the red answers are incorrect?
Wait — let’s look at Problem 4:
Problem 4:
-1 + 6x + 2x
→ 6x + 2x = 8x; constant -1
✔ Should be: 8x - 1
But red answer says: 14x + 11 — again, doesn’t match.
This suggests that either:
- The problems were miswritten in transcription, OR
- The red answers are for different problems.
Looking back at your initial message, you listed:
> 1) 5x + 5 + 2x → 7x + 5 ✔ matches
> 2) -3 + 9x + 8 → 17x + 11 ✘ doesn't match
> 3) 17x + 11 → 17x + 11 ✔
> 4) -1 + 6x + 2x → 14x + 11 ✘
Wait — perhaps the numbering is off? Or maybe some problems have more terms?
Let me try to reconstruct from common patterns.
Alternatively — maybe the user intended to provide the *correct* answers in red, and we should verify them? But the instruction is to solve accurately.
Given the confusion, I will solve each expression exactly as written in your list, ignoring the red answers if they don’t match, because our job is to compute correctly.
So let’s proceed systematically.
---
Solving Each Problem Accurately:
1) 5x + 5 + 2x
= (5x + 2x) + 5 = 7x + 5
2) -3 + 9x + 8
= 9x + (-3 + 8) = 9x + 5
3) 17x + 11
Already simplified → 17x + 11
4) -1 + 6x + 2x
= (6x + 2x) + (-1) = 8x - 1
5) 9x + 5 - 7x + 4
= (9x - 7x) + (5 + 4) = 2x + 9
6) 14x + 3 - 6 - 7f
Wait — here we have ‘f’ and ‘x’. Are they different variables? Yes. So we cannot combine x and f terms.
So: 14x - 7f + (3 - 6) = 14x - 7f - 3
But red answer says: “15x - 7f - 6” — which would require 14x + x? Not present. Also 3-6=-3, not -6.
Unless it’s a typo and should be “14x + x - 6 - 7f”? But as written: 14x - 7f - 3
Hmm. This is getting messy. Perhaps the original problems had typos or misalignments.
To avoid further confusion, I will assume that the expressions are written correctly in your list, and solve them as-is, even if the red answers differ.
Let’s continue.
7) 13x + 7 + 10 - u
Variables: x and u — different, so keep separate.
Constants: 7 + 10 = 17
So: 13x - u + 17
Red answer says: “15x + 10u + 19” — completely different. So likely mismatched.
I think the best approach is to ignore the red answers and solve the expressions as given in your numbered list.
Let me rewrite all 16 problems clearly and solve each:
---
Correct Solutions:
1) 5x + 5 + 2x = 7x + 5
2) -3 + 9x + 8 = 9x + 5
3) 17x + 11 = 17x + 11
4) -1 + 6x + 2x = 8x - 1
5) 9x + 5 - 7x + 4 = (9x - 7x) + (5 + 4) = 2x + 9
6) 14x + 3 - 6 - 7f = 14x - 7f - 3 *(since 3-6=-3)*
7) 13x + 7 + 10 - u = 13x - u + 17
8) 2x + 4 + 6x + 9 = (2x + 6x) + (4 + 9) = 8x + 13
Wait — in your list, #8 is: “2x + 4 + 6x + 9” → yes.
But earlier you had up to #7, then jumped? Let me check your original input:
You wrote:
> 1) ...
> 2) ...
> 3) ...
> 4) ...
> 5) ...
> 6) ...
> 7) ...
> 8) 2x + 4 + 6x + 9 → 7x + 8 + 15 ← wait, that doesn’t make sense.
Actually, looking back:
In your very first message, after #7, you have:
> 8) 2x + 4 + 6x + 9
> 7x + 8 + 15 ← this seems like two lines? Or maybe it's "7x + 8" and "+15" is next?
No — let's parse your original text carefully:
You wrote:
```
1) 5x + 5 + 2x 7x + 5
2) -3 + 9x + 8 17x + 11
3) 17x + 11 17x + 11
4) -1 + 6x + 2x 14x + 11
5) 9x + 5 - 7x + 4 2x + 9
6) 14x + 3 - 6 - 7f 15x - 7f - 6
7) 13x + 7 + 10 - u 15x + 10u + 19
8) 2x + 4 + 6x + 9 7x + 8 + 15
```
Oh! I see now — the second column is the student's answer (in red), which may be wrong. Our job is to provide the correct answer.
So for each row, left side is the expression, right side is possibly incorrect answer. We need to simplify the left side correctly.
So let's do that for all 16.
List of expressions to simplify:
1. 5x + 5 + 2x
2. -3 + 9x + 8
3. 17x + 11
4. -1 + 6x + 2x
5. 9x + 5 - 7x + 4
6. 14x + 3 - 6 - 7f
7. 13x + 7 + 10 - u
8. 2x + 4 + 6x + 9
9. 2x + 4 + 6x + 9 + 4y ← wait, in your list, #9 is: "2x + 4 + 6x + 9 + 4y" ? Let's see:
From your text:
After #8, you have:
> 9) 2x + 4 + 6x + 9 + 4y
> 7x + 8 + 15 + 4y ← again, probably student's answer
Actually, let's extract all 16 expressions from your message:
You wrote:
```
1) 5x + 5 + 2x
2) -3 + 9x + 8
3) 17x + 11
4) -1 + 6x + 2x
5) 9x + 5 - 7x + 4
6) 14x + 3 - 6 - 7f
7) 13x + 7 + 10 - u
8) 2x + 4 + 6x + 9
9) 2x + 4 + 6x + 9 + 4y [assuming from context]
10) 2x + 4 + 6x + 9 + 4y + 6z ? Wait, no.
Let's copy-paste your exact list:
From your initial post:
"1) 5x + 5 + 2x 7x + 5
2) -3 + 9x + 8 17x + 11
3) 17x + 11 17x + 11
4) -1 + 6x + 2x 14x + 11
5) 9x + 5 - 7x + 4 2x + 9
6) 14x + 3 - 6 - 7f 15x - 7f - 6
7) 13x + 7 + 10 - u 15x + 10u + 19
8) 2x + 4 + 6x + 9 7x + 8 + 15
9) 2x + 4 + 6x + 9 + 4y 7x + 8 + 15 + 4y
10) 2x + 4 + 6x + 9 + 4y + 6z 7x + 8 + 15 + 4y + 6z
11) 14p + 2(2p + 4) + 4 26p + 2(2p + 4)
12) 2h + 4 + 12h + 4 + 9y 17h + 23y + 18
13) 23v + 4 + 12v + 7 + 2h + 1 9v + 2h + 1
14) 5t + v + 7t 2t + 8v
15) 13x + 2y + 6y - 1 19x + 4y - 1
16) 4x + 5x² + 4x + 10x² 15x² + 9x"
Okay, now I have all 16 expressions. The right-hand side is the student's answer, which may be incorrect. We will simplify the left-hand side correctly.
Let's solve each one step by step.
---
1) 5x + 5 + 2x
Combine x terms: 5x + 2x = 7x
Constant: 5
→ 7x + 5
2) -3 + 9x + 8
Constants: -3 + 8 = 5
Variable: 9x
→ 9x + 5
3) 17x + 11
No like terms to combine.
→ 17x + 11
4) -1 + 6x + 2x
x terms: 6x + 2x = 8x
Constant: -1
→ 8x - 1
5) 9x + 5 - 7x + 4
x terms: 9x - 7x = 2x
Constants: 5 + 4 = 9
→ 2x + 9
6) 14x + 3 - 6 - 7f
x term: 14x
f term: -7f
Constants: 3 - 6 = -3
→ 14x - 7f - 3
7) 13x + 7 + 10 - u
x term: 13x
u term: -u
Constants: 7 + 10 = 17
→ 13x - u + 17
8) 2x + 4 + 6x + 9
x terms: 2x + 6x = 8x
Constants: 4 + 9 = 13
→ 8x + 13
9) 2x + 4 + 6x + 9 + 4y
x terms: 2x + 6x = 8x
y term: 4y
Constants: 4 + 9 = 13
→ 8x + 4y + 13
10) 2x + 4 + 6x + 9 + 4y + 6z
x terms: 2x + 6x = 8x
y term: 4y
z term: 6z
Constants: 4 + 9 = 13
→ 8x + 4y + 6z + 13
11) 14p + 2(2p + 4) + 4
First, distribute the 2: 2 * 2p = 4p, 2 * 4 = 8
So: 14p + 4p + 8 + 4
Now combine p terms: 14p + 4p = 18p
Constants: 8 + 4 = 12
→ 18p + 12
12) 2h + 4 + 12h + 4 + 9y
h terms: 2h + 12h = 14h
y term: 9y
Constants: 4 + 4 = 8
→ 14h + 9y + 8
13) 23v + 4 + 12v + 7 + 2h + 1
v terms: 23v + 12v = 35v
h term: 2h
Constants: 4 + 7 + 1 = 12
→ 35v + 2h + 12
14) 5t + v + 7t
t terms: 5t + 7t = 12t
v term: v
→ 12t + v
15) 13x + 2y + 6y - 1
x term: 13x
y terms: 2y + 6y = 8y
Constant: -1
→ 13x + 8y - 1
16) 4x + 5x² + 4x + 10x²
x² terms: 5x² + 10x² = 15x²
x terms: 4x + 4x = 8x
→ 15x² + 8x
---
Now, let's compile the correct answers:
1. 7x + 5
2. 9x + 5
3. 17x + 11
4. 8x - 1
5. 2x + 9
6. 14x - 7f - 3
7. 13x - u + 17
8. 8x + 13
9. 8x + 4y + 13
10. 8x + 4y + 6z + 13
11. 18p + 12
12. 14h + 9y + 8
13. 35v + 2h + 12
14. 12t + v
15. 13x + 8y - 1
16. 15x² + 8x
Note: In problem 16, the student's answer was "15x² + 9x", but we have 4x + 4x = 8x, not 9x. So correct is 8x.
Also, in problem 11, student had "26p + 2(2p + 4)" which is not simplified — we distributed and combined.
All done.
Final Answer:
1. 7x + 5
2. 9x + 5
3. 17x + 11
4. 8x - 1
5. 2x + 9
6. 14x - 7f - 3
7. 13x - u + 17
8. 8x + 13
9. 8x + 4y + 13
10. 8x + 4y + 6z + 13
11. 18p + 12
12. 14h + 9y + 8
13. 35v + 2h + 12
14. 12t + v
15. 13x + 8y - 1
16. 15x² + 8x
Parent Tip: Review the logic above to help your child master the concept of combining like terms worksheet answers.
