Solving Equations by Combining Like Terms Practice 2 worksheet ... - Free Printable

Let’s solve each equation one by one. We’ll combine like terms and isolate the variable step by step.

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1. –8r – 7r = 15

Combine the r terms:
–8r – 7r = –15r
So:
–15r = 15
Divide both sides by –15:
r = 15 ÷ (–15) = –1

✔ Check: –8(–1) – 7(–1) = 8 + 7 = 15 → Correct.

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2. –7x + 6 + 5x = 14

Combine x terms: –7x + 5x = –2x
So:
–2x + 6 = 14
Subtract 6 from both sides:
–2x = 8
Divide by –2:
x = 8 ÷ (–2) = –4

✔ Check: –7(–4) + 6 + 5(–4) = 28 + 6 – 20 = 14 → Correct.

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3. 10 = 3x + 3 + 4x

Combine x terms: 3x + 4x = 7x
So:
10 = 7x + 3
Subtract 3 from both sides:
7 = 7x
Divide by 7:
x = 1

✔ Check: 3(1) + 3 + 4(1) = 3 + 3 + 4 = 10 → Correct.

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4. –4(–3 + 3p) + 7 = 91

First, distribute –4:
–4 × –3 = 12
–4 × 3p = –12p
So:
12 – 12p + 7 = 91
Combine constants: 12 + 7 = 19
So:
19 – 12p = 91
Subtract 19 from both sides:
–12p = 72
Divide by –12:
p = 72 ÷ (–12) = –6

✔ Check: –4(–3 + 3×–6) + 7 = –4(–3 –18) + 7 = –4(–21) + 7 = 84 + 7 = 91 → Correct.

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5. 97 = 5m + 6(1 – 3m)

Distribute 6:
6 × 1 = 6
6 × –3m = –18m
So:
97 = 5m + 6 – 18m
Combine m terms: 5m – 18m = –13m
So:
97 = –13m + 6
Subtract 6:
91 = –13m
Divide by –13:
m = 91 ÷ (–13) = –7

✔ Check: 5(–7) + 6(1 – 3×–7) = –35 + 6(1 + 21) = –35 + 6×22 = –35 + 132 = 97 → Correct.

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6. 4(4 – 6p) + 5 = 93

Distribute 4:
4×4 = 16
4×–6p = –24p
So:
16 – 24p + 5 = 93
Combine constants: 16 + 5 = 21
So:
21 – 24p = 93
Subtract 21:
–24p = 72
Divide by –24:
p = 72 ÷ (–24) = –3

✔ Check: 4(4 – 6×–3) + 5 = 4(4 + 18) + 5 = 4×22 + 5 = 88 + 5 = 93 → Correct.

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7. 6m – 7(5m + 4) = –202

Distribute –7:
–7×5m = –35m
–7×4 = –28
So:
6m – 35m – 28 = –202
Combine m terms: 6m – 35m = –29m
So:
–29m – 28 = –202
Add 28 to both sides:
–29m = –174
Divide by –29:
m = –174 ÷ (–29) = 6

✔ Check: 6(6) – 7(5×6 + 4) = 36 – 7(30 + 4) = 36 – 7×34 = 36 – 238 = –202 → Correct.

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8. 8(–7k + 4) – 3(1 + 5k) = –42

Distribute 8:
8×–7k = –56k
8×4 = 32
Distribute –3:
–3×1 = –3
–3×5k = –15k
So:
–56k + 32 – 3 – 15k = –42
Combine k terms: –56k – 15k = –71k
Combine constants: 32 – 3 = 29
So:
–71k + 29 = –42
Subtract 29:
–71k = –71
Divide by –71:
k = –1

✔ Check: 8(–7×–1 + 4) – 3(1 + 5×–1) = 8(7 + 4) – 3(1 – 5) = 8×11 – 3×(–4) = 88 + 12 = 100? Wait — that’s not right!

Wait — let me recalculate check:

Original: 8(–7k + 4) – 3(1 + 5k) with k = –1

Inside first parentheses: –7(–1) + 4 = 7 + 4 = 11 → 8×11 = 88
Second: 1 + 5(–1) = 1 – 5 = –4 → –3×(–4) = +12
Total: 88 + 12 = 100 ≠ –42 → ERROR!

I made a mistake in solving.

Go back:

Equation after distributing:

–56k + 32 – 3 – 15k = –42
→ –71k + 29 = –42
Then: –71k = –42 – 29 = –71
So k = (–71)/(–71) = 1? Wait no:

–71k = –71 → k = 1? But earlier I said k = –1.

Wait — if –71k = –71, then k = 1.

But when I checked with k = –1, I got 100, which is wrong.

Try k = 1:

8(–7×1 + 4) – 3(1 + 5×1) = 8(–7+4) – 3(6) = 8(–3) – 18 = –24 – 18 = –42 → YES!

So I had a sign error in my division.

From: –71k = –71 → divide both sides by –71 → k = 1

Earlier I wrote k = –1 by mistake.

Correct answer: k = 1

✔ Final check: as above → –42 → Correct.

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9. –5(1 – 8r) + 7(1 – r) = –31

Distribute –5:
–5×1 = –5
–5×–8r = +40r
Distribute 7:
7×1 = 7
7×–r = –7r
So:
–5 + 40r + 7 – 7r = –31
Combine r terms: 40r – 7r = 33r
Combine constants: –5 + 7 = 2
So:
33r + 2 = –31
Subtract 2:
33r = –33
Divide by 33:
r = –1

✔ Check: –5(1 – 8×–1) + 7(1 – –1) = –5(1+8) + 7(2) = –5×9 + 14 = –45 + 14 = –31 → Correct.

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10. –4(2x + 1) + 6(4 + 4x) = –60

Distribute –4:
–4×2x = –8x
–4×1 = –4
Distribute 6:
6×4 = 24
6×4x = 24x
So:
–8x – 4 + 24 + 24x = –60
Combine x terms: –8x + 24x = 16x
Combine constants: –4 + 24 = 20
So:
16x + 20 = –60
Subtract 20:
16x = –80
Divide by 16:
x = –80 ÷ 16 = –5

✔ Check: –4(2×–5 + 1) + 6(4 + 4×–5) = –4(–10+1) + 6(4–20) = –4(–9) + 6(–16) = 36 – 96 = –60 → Correct.

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Final Answer:
1. r = –1
2. x = –4
3. x = 1
4. p = –6
5. m = –7
6. p = –3
7. m = 6
8. k = 1
9. r = –1
10. x = –5