One-step equations worksheet focusing on positive integers, featuring 12 problems to solve.
Worksheet titled "One-Step Equations: Positive Integers" with 12 equations to solve, including variables and positive integers, from Math Monks.
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Step-by-step solution for: One Step Equations Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: One Step Equations Worksheets - Math Monks
Let’s solve each equation one by one. Remember, we want to find the value of the letter (variable) that makes the equation true. We do this by doing the opposite operation to both sides — like if something is added, we subtract it from both sides; if something is multiplied, we divide both sides by it.
---
1. 2 + q = 16
We want to get “q” alone. Since 2 is added to q, we subtract 2 from both sides:
q = 16 - 2
→ q = 14
---
2. 121 = 11a
“a” is being multiplied by 11. To undo that, divide both sides by 11:
a = 121 ÷ 11
→ a = 11
---
3. x/5 = 100
x is divided by 5. Multiply both sides by 5:
x = 100 × 5
→ x = 500
---
4. 19 = 3 + q
Subtract 3 from both sides:
q = 19 - 3
→ q = 16
---
5. p + 17 = 27
Subtract 17 from both sides:
p = 27 - 17
→ p = 10
---
6. 14 = 2w
Divide both sides by 2:
w = 14 ÷ 2
→ w = 7
---
7. 4/(3x) = 15
This one looks tricky. Let’s think: 4 divided by (3 times x) equals 15.
First, multiply both sides by (3x) to get rid of the denominator:
4 = 15 × 3x
→ 4 = 45x
Now divide both sides by 45:
x = 4 ÷ 45
→ x = 4/45
*(Note: This is a fraction — and it’s correct! The problem says “positive integers”, but sometimes equations give fractions as answers. Maybe there was a typo in the worksheet? But mathematically, this is right.)*
Wait — let me double-check. If the equation is written as “4 over 3x = 15”, then yes, x = 4/45.
But maybe it was meant to be (4/3)x = 15? That would make more sense for positive integers.
Let’s check both interpretations.
If it’s (4/3)x = 15, then:
Multiply both sides by 3:
4x = 45
Then divide by 4:
x = 45/4 → still not integer.
Hmm. Or maybe it’s 4 divided by (3x) = 15 → which gives x = 4/45.
Since the title says “Positive Integers”, perhaps this is an error in the worksheet. But we’ll go with what’s written.
Actually — wait! Looking again at the image: it says “4 / 3x = 15”. In many worksheets, this might mean (4/3) * x = 15. Let’s assume that’s the case because otherwise the answer isn’t an integer.
So let’s try:
(4/3)x = 15
Multiply both sides by 3:
4x = 45
Divide by 4:
x = 45/4 → still not integer.
That doesn’t work either.
Alternative: Maybe it’s 4 divided by (3x) = 15 → x = 4/45.
I think we have to accept that — unless there’s a misprint.
But let’s look at the original image description — user said “positive integers”, so maybe #7 is meant to be different.
Wait — another possibility: maybe it’s “4 over 3” times x = 15? Same as above.
Or perhaps it’s “4 = 3x * 15”? No, that doesn’t match.
Let me re-read: “7. 4 / 3x = 15”
In standard math notation, without parentheses, “4 / 3x” usually means 4 divided by (3x). So:
4 / (3x) = 15
→ 4 = 15 * 3x
→ 4 = 45x
→ x = 4/45
It’s not an integer. But since the worksheet says “positive integers”, maybe it’s a mistake. However, for accuracy, I’ll keep it as x = 4/45.
But let’s hold on — maybe I should check other problems first and come back.
---
8. 3 = 7p + 5
Subtract 5 from both sides:
3 - 5 = 7p
→ -2 = 7p
Divide by 7:
p = -2/7
Again, negative and fractional — contradicts “positive integers”.
This suggests there may be typos in the worksheet. But let’s continue solving as written.
Wait — maybe the equation is 3 = 7p + 5, but perhaps it’s supposed to be 3 + 5 = 7p? No, that’s not what’s written.
Alternatively, maybe it’s 3 = 7(p + 5)? But no parentheses shown.
Given the instructions, I must solve as written.
So:
3 = 7p + 5
→ 3 - 5 = 7p
→ -2 = 7p
→ p = -2/7
Not positive integer. Hmm.
Perhaps the worksheet has errors. But let’s proceed.
---
9. 7s = 147
Divide both sides by 7:
s = 147 ÷ 7
→ s = 21
---
10. 4y = 12
Divide by 4:
y = 12 ÷ 4
→ y = 3
---
11. 11 = b/2
Multiply both sides by 2:
b = 11 × 2
→ b = 22
---
12. 16 = n + 6
Subtract 6:
n = 16 - 6
→ n = 10
---
Now going back to #7 and #8 — they don’t yield positive integers. Let me double-check #7.
Looking at the original image description: “7. 4 / 3x = 15”
What if it’s actually “(4/3)x = 15”? Then:
x = 15 * 3 / 4 = 45/4 = 11.25 — still not integer.
What if it’s “4 = 3x * 15”? Then 4 = 45x → same as before.
Another idea: maybe it’s “4 over 3” equals 15/x? But that’s not what’s written.
Perhaps it’s a formatting issue — maybe it’s “4/3 x = 15” meaning (4/3)*x=15, but again, not integer.
Wait — what if the equation is “4 = 3x + 15”? Then:
4 - 15 = 3x → -11 = 3x → x = -11/3 — worse.
I think we have to conclude that #7 and #8 are either misprinted or intentionally include non-integers, despite the title.
But let’s look at #8 again: “3 = 7p + 5”
If we rearrange: 7p = 3 - 5 = -2 → p = -2/7
No way around it.
Perhaps the worksheet meant “3 + 5 = 7p” → 8 = 7p → p = 8/7 — still not integer.
Or “3 = 7p - 5” → 8 = 7p → p = 8/7.
Still not.
Maybe “13 = 7p + 5” → 8 = 7p → no.
I think for the sake of completing the task, I’ll provide the mathematical solutions as written, even if they’re not positive integers.
But let’s verify all calculations once more.
---
Recalculating all:
1. 2 + q = 16 → q = 14 ✔
2. 121 = 11a → a = 11 ✔
3. x/5 = 100 → x = 500 ✔
4. 19 = 3 + q → q = 16 ✔
5. p + 17 = 27 → p = 10 ✔
6. 14 = 2w → w = 7 ✔
7. 4/(3x) = 15 → 4 = 45x → x = 4/45 ✔ (mathematically correct)
8. 3 = 7p + 5 → 7p = -2 → p = -2/7 ✔
9. 7s = 147 → s = 21 ✔
10. 4y = 12 → y = 3 ✔
11. 11 = b/2 → b = 22 ✔
12. 16 = n + 6 → n = 10 ✔
Even though #7 and #8 don't give positive integers, they are solved correctly based on the given equations.
Final Answer:
1. q = 14
2. a = 11
3. x = 500
4. q = 16
5. p = 10
6. w = 7
7. x = 4/45
8. p = -2/7
9. s = 21
10. y = 3
11. b = 22
12. n = 10
---
1. 2 + q = 16
We want to get “q” alone. Since 2 is added to q, we subtract 2 from both sides:
q = 16 - 2
→ q = 14
---
2. 121 = 11a
“a” is being multiplied by 11. To undo that, divide both sides by 11:
a = 121 ÷ 11
→ a = 11
---
3. x/5 = 100
x is divided by 5. Multiply both sides by 5:
x = 100 × 5
→ x = 500
---
4. 19 = 3 + q
Subtract 3 from both sides:
q = 19 - 3
→ q = 16
---
5. p + 17 = 27
Subtract 17 from both sides:
p = 27 - 17
→ p = 10
---
6. 14 = 2w
Divide both sides by 2:
w = 14 ÷ 2
→ w = 7
---
7. 4/(3x) = 15
This one looks tricky. Let’s think: 4 divided by (3 times x) equals 15.
First, multiply both sides by (3x) to get rid of the denominator:
4 = 15 × 3x
→ 4 = 45x
Now divide both sides by 45:
x = 4 ÷ 45
→ x = 4/45
*(Note: This is a fraction — and it’s correct! The problem says “positive integers”, but sometimes equations give fractions as answers. Maybe there was a typo in the worksheet? But mathematically, this is right.)*
Wait — let me double-check. If the equation is written as “4 over 3x = 15”, then yes, x = 4/45.
But maybe it was meant to be (4/3)x = 15? That would make more sense for positive integers.
Let’s check both interpretations.
If it’s (4/3)x = 15, then:
Multiply both sides by 3:
4x = 45
Then divide by 4:
x = 45/4 → still not integer.
Hmm. Or maybe it’s 4 divided by (3x) = 15 → which gives x = 4/45.
Since the title says “Positive Integers”, perhaps this is an error in the worksheet. But we’ll go with what’s written.
Actually — wait! Looking again at the image: it says “4 / 3x = 15”. In many worksheets, this might mean (4/3) * x = 15. Let’s assume that’s the case because otherwise the answer isn’t an integer.
So let’s try:
(4/3)x = 15
Multiply both sides by 3:
4x = 45
Divide by 4:
x = 45/4 → still not integer.
That doesn’t work either.
Alternative: Maybe it’s 4 divided by (3x) = 15 → x = 4/45.
I think we have to accept that — unless there’s a misprint.
But let’s look at the original image description — user said “positive integers”, so maybe #7 is meant to be different.
Wait — another possibility: maybe it’s “4 over 3” times x = 15? Same as above.
Or perhaps it’s “4 = 3x * 15”? No, that doesn’t match.
Let me re-read: “7. 4 / 3x = 15”
In standard math notation, without parentheses, “4 / 3x” usually means 4 divided by (3x). So:
4 / (3x) = 15
→ 4 = 15 * 3x
→ 4 = 45x
→ x = 4/45
It’s not an integer. But since the worksheet says “positive integers”, maybe it’s a mistake. However, for accuracy, I’ll keep it as x = 4/45.
But let’s hold on — maybe I should check other problems first and come back.
---
8. 3 = 7p + 5
Subtract 5 from both sides:
3 - 5 = 7p
→ -2 = 7p
Divide by 7:
p = -2/7
Again, negative and fractional — contradicts “positive integers”.
This suggests there may be typos in the worksheet. But let’s continue solving as written.
Wait — maybe the equation is 3 = 7p + 5, but perhaps it’s supposed to be 3 + 5 = 7p? No, that’s not what’s written.
Alternatively, maybe it’s 3 = 7(p + 5)? But no parentheses shown.
Given the instructions, I must solve as written.
So:
3 = 7p + 5
→ 3 - 5 = 7p
→ -2 = 7p
→ p = -2/7
Not positive integer. Hmm.
Perhaps the worksheet has errors. But let’s proceed.
---
9. 7s = 147
Divide both sides by 7:
s = 147 ÷ 7
→ s = 21
---
10. 4y = 12
Divide by 4:
y = 12 ÷ 4
→ y = 3
---
11. 11 = b/2
Multiply both sides by 2:
b = 11 × 2
→ b = 22
---
12. 16 = n + 6
Subtract 6:
n = 16 - 6
→ n = 10
---
Now going back to #7 and #8 — they don’t yield positive integers. Let me double-check #7.
Looking at the original image description: “7. 4 / 3x = 15”
What if it’s actually “(4/3)x = 15”? Then:
x = 15 * 3 / 4 = 45/4 = 11.25 — still not integer.
What if it’s “4 = 3x * 15”? Then 4 = 45x → same as before.
Another idea: maybe it’s “4 over 3” equals 15/x? But that’s not what’s written.
Perhaps it’s a formatting issue — maybe it’s “4/3 x = 15” meaning (4/3)*x=15, but again, not integer.
Wait — what if the equation is “4 = 3x + 15”? Then:
4 - 15 = 3x → -11 = 3x → x = -11/3 — worse.
I think we have to conclude that #7 and #8 are either misprinted or intentionally include non-integers, despite the title.
But let’s look at #8 again: “3 = 7p + 5”
If we rearrange: 7p = 3 - 5 = -2 → p = -2/7
No way around it.
Perhaps the worksheet meant “3 + 5 = 7p” → 8 = 7p → p = 8/7 — still not integer.
Or “3 = 7p - 5” → 8 = 7p → p = 8/7.
Still not.
Maybe “13 = 7p + 5” → 8 = 7p → no.
I think for the sake of completing the task, I’ll provide the mathematical solutions as written, even if they’re not positive integers.
But let’s verify all calculations once more.
---
Recalculating all:
1. 2 + q = 16 → q = 14 ✔
2. 121 = 11a → a = 11 ✔
3. x/5 = 100 → x = 500 ✔
4. 19 = 3 + q → q = 16 ✔
5. p + 17 = 27 → p = 10 ✔
6. 14 = 2w → w = 7 ✔
7. 4/(3x) = 15 → 4 = 45x → x = 4/45 ✔ (mathematically correct)
8. 3 = 7p + 5 → 7p = -2 → p = -2/7 ✔
9. 7s = 147 → s = 21 ✔
10. 4y = 12 → y = 3 ✔
11. 11 = b/2 → b = 22 ✔
12. 16 = n + 6 → n = 10 ✔
Even though #7 and #8 don't give positive integers, they are solved correctly based on the given equations.
Final Answer:
1. q = 14
2. a = 11
3. x = 500
4. q = 16
5. p = 10
6. w = 7
7. x = 4/45
8. p = -2/7
9. s = 21
10. y = 3
11. b = 22
12. n = 10
Parent Tip: Review the logic above to help your child master the concept of writing one step equations worksheet.
