Worksheet for solving multi-step equations with algebra problems.

Let’s solve each equation step by step. We’ll combine like terms first, then isolate the variable.

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1. 3m + 2m - 5 = 20

Combine like terms:
3m + 2m = 5m → so we have:
5m - 5 = 20

Add 5 to both sides:
5m = 25

Divide by 5:
m = 5

✔ Check: 3(5) + 2(5) - 5 = 15 + 10 - 5 = 20 ✔️

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2. 0.8a + 0.3a - 0.5 = 17

Combine like terms:
0.8a + 0.3a = 1.1a → so:
1.1a - 0.5 = 17

Add 0.5 to both sides:
1.1a = 17.5

Divide by 1.1:
a = 17.5 ÷ 1.1 = 175 ÷ 11 ≈ 15.909... but let’s keep it exact:
a = 175/11 or as a mixed number: 15 10/11

But wait — maybe we should check if this is meant to be decimal-friendly? Let’s double-check:

Actually, 1.1a = 17.5 → multiply numerator and denominator by 10:
11a = 175 → a = 175 ÷ 11 = 15.909... That’s correct.

But perhaps the problem expects an exact fraction? Or maybe I made a mistake?

Wait — let me recalculate:

Original: 0.8a + 0.3a = 1.1a → yes
Then 1.1a = 17.5 → yes
So a = 17.5 / 1.1 = 175/11 → that’s correct.

We can leave it as a fraction: a = 175/11

Or as a decimal rounded? But since others are whole numbers, maybe I misread?

Wait — let me check original again: “0.8a + 0.3a - 0.5 = 17”

Yes. So unless there's a typo in the problem, answer is 175/11.

But let’s hold on — maybe we can write it as a decimal for now? Actually, better to keep exact.

Alternatively, perhaps the problem intended integers? Let’s proceed and see other problems.

Actually, let’s just go with exact value.

But wait — let me try solving numerically:

1.1a = 17.5 → a = 17.5 ÷ 1.1 = 15.909090...

Hmm. Maybe it’s okay. Let’s move on and come back if needed.

Actually, let’s do all problems first.

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3. 6 + 2a + 5 = 9

Combine constants: 6 + 5 = 11 → so:
2a + 11 = 9

Subtract 11 from both sides:
2a = -2

Divide by 2:
a = -1

✔ Check: 6 + 2(-1) + 5 = 6 - 2 + 5 = 9 ✔️

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4. 30 = 5y - 3y + 8

Combine like terms: 5y - 3y = 2y → so:
30 = 2y + 8

Subtract 8 from both sides:
22 = 2y

Divide by 2:
y = 11

✔ Check: 5(11) - 3(11) + 8 = 55 - 33 + 8 = 30 ✔️

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5. 12 + 0.6d + 8 = 20

Combine constants: 12 + 8 = 20 → so:
0.6d + 20 = 20

Subtract 20 from both sides:
0.6d = 0

Divide by 0.6:
d = 0

✔ Check: 12 + 0.6(0) + 8 = 20 ✔️

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6. 2c + 3c - 8 = 22

Combine like terms: 2c + 3c = 5c → so:
5c - 8 = 22

Add 8 to both sides:
5c = 30

Divide by 5:
c = 6

✔ Check: 2(6) + 3(6) - 8 = 12 + 18 - 8 = 22 ✔️

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7. 15 = 6b - 2.5b + 1

Combine like terms: 6b - 2.5b = 3.5b → so:
15 = 3.5b + 1

Subtract 1 from both sides:
14 = 3.5b

Divide by 3.5:
b = 14 ÷ 3.5 = 4

✔ Check: 6(4) - 2.5(4) + 1 = 24 - 10 + 1 = 15 ✔️

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8. 21 = 3 + 2x + 9

Combine constants: 3 + 9 = 12 → so:
21 = 2x + 12

Subtract 12 from both sides:
9 = 2x

Divide by 2:
x = 4.5 or 9/2

✔ Check: 3 + 2(4.5) + 9 = 3 + 9 + 9 = 21 ✔️

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Now back to #2: 0.8a + 0.3a - 0.5 = 17

We had: 1.1a = 17.5 → a = 17.5 / 1.1

Let me compute that exactly:

17.5 ÷ 1.1 = (175/10) ÷ (11/10) = 175/10 × 10/11 = 175/11

175 ÷ 11 = 15 with remainder 10 → so 15 10/11

As decimal: 15.909090... repeating

But since other answers are nice, maybe the problem has a typo? Or perhaps it’s acceptable.

Wait — let me re-read the original image text: “0.8a + 0.3a - 0.5 = 17”

Yes. So unless it’s supposed to be 0.8a + 0.2a or something else, we must go with what’s written.

Perhaps they expect fractional form? Let’s write it as fraction.

But looking at problem #5 and #7, decimals are used and give integer answers, so maybe #2 is also meant to be clean? Let me check calculation again.

0.8a + 0.3a = 1.1a — correct
1.1a - 0.5 = 17 → 1.1a = 17.5 — correct
a = 17.5 / 1.1

Multiply numerator and denominator by 10: 175 / 11 — which is approximately 15.909, but not integer.

Maybe it’s fine. Perhaps the worksheet includes non-integer answers.

Alternatively, maybe I should express it as a decimal rounded? But no instruction.

I think we should present exact value: a = 175/11 or 15 10/11

But let’s see — in context of middle school math, sometimes they avoid fractions like this. Wait — perhaps I miscalculated the combination?

0.8 + 0.3 is definitely 1.1 — yes.

Another thought: maybe the equation is 0.8a + 0.3a - 0.5 = 1.7? But no, it says 17.

Looking back at user input: “2. 0.8a + 0.3a - 0.5 = 17” — yes.

So I’ll go with a = 175/11

But to make it neat, perhaps write as mixed number or decimal? Since others are integers or simple decimals, maybe decimal is okay.

In problem #8, x=4.5 is acceptable.

So for consistency, let’s write a = 15.909... but that’s messy.

Wait — 175 ÷ 11 = 15.909090... which is 15.\overline{90}

But perhaps better to leave as fraction.

Actually, let me calculate numerically:

1.1 * 15.909090... = 1.1 * (175/11) = (11/10)*(175/11) = 175/10 = 17.5 — yes, then minus 0.5 is 17 — correct.

So it’s correct.

I think for the answer, we can write it as a fraction or decimal. Since the problem uses decimals, maybe decimal is fine, but it’s repeating.

Alternatively, perhaps the problem meant 0.8a + 0.2a? Then it would be 1.0a - 0.5 = 17 → a = 17.5 — still not integer.

Or if it was 0.7a + 0.3a = 1.0a, same thing.

Wait — what if it’s 0.8a + 0.3a = 1.1a, and 1.1a = 17.5, so a = 17.5 / 1.1 = 175/11 — I think we have to accept it.

Perhaps in the context, they want exact fraction.

But let’s look at the other problems — all others give integer or half-integer answers except this one.

Problem #8 gave 4.5, which is fine.

So for #2, I’ll write a = 175/11 or approximately 15.91, but since it’s math, exact is better.

Actually, let me see if 175/11 reduces — no, 175 and 11 share no common factors.

So final decision: for #2, a = 175/11

But to match format, perhaps write as decimal? No, better exact.

Wait — another idea: maybe the equation is 0.8a + 0.3a - 0.5 = 1.7? But user wrote 17.

Looking at user input: “2. 0.8a + 0.3a - 0.5 = 17” — yes.

I think we proceed.

So summarizing all answers:

1. m = 5
2. a = 175/11 or 15 10/11
3. a = -1
4. y = 11
5. d = 0
6. c = 6
7. b = 4
8. x = 4.5 or 9/2

For #2, since it's unusual, but correct, I'll box it as fraction.

But let me confirm once more:

Equation 2: 0.8a + 0.3a = 1.1a; 1.1a - 0.5 = 17 → 1.1a = 17.5 → a = 17.5 / 1.1

17.5 divided by 1.1: move decimal: 175 divided by 11 = 15.9090... yes.

Perhaps write as \frac{175}{11}

In the final answer, I'll list them clearly.

Also, for #8, x=4.5 is fine.

Now, compiling final answers:

Final Answer:
1. m = 5
2. a = \frac{175}{11}
3. a = -1
4. y = 11
5. d = 0
6. c = 6
7. b = 4
8. x = \frac{9}{2} or 4.5

To be consistent, perhaps use fractions where needed.

Since #8 is 9/2, and #2 is 175/11, that's fine.

Some might prefer decimals, but fractions are exact.

I think this is correct.