Linear Equations Worksheets with Answer Key - Free Printable

Let’s solve each equation one by one, step by step. We’ll isolate the variable on one side of the equation and simplify.

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Problem 1: 12 - x = 7

Subtract 12 from both sides:
- x = 7 - 12
→ -x = -5

Multiply both sides by -1:
→ x = 5

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Problem 2: 9 + 6x = 3x + 13

Subtract 3x from both sides:
→ 9 + 3x = 13

Subtract 9 from both sides:
→ 3x = 4

Divide by 3:
→ x = 4/3 (or 1.333...)

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Problem 3: 10x + 3 + 10x = 13x - 3

Combine like terms on left:
→ 20x + 3 = 13x - 3

Subtract 13x from both sides:
→ 7x + 3 = -3

Subtract 3 from both sides:
→ 7x = -6

Divide by 7:
→ x = -6/7

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Problem 4: 0.25(60) + 0.10x = 0.15(60 + x)

First, calculate 0.25 × 60 = 15
And expand right side: 0.15×60 + 0.15x = 9 + 0.15x

So equation becomes:
→ 15 + 0.10x = 9 + 0.15x

Subtract 0.10x from both sides:
→ 15 = 9 + 0.05x

Subtract 9:
→ 6 = 0.05x

Divide by 0.05:
→ x = 6 ÷ 0.05 = 120

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Problem 5: 3 = 4(x - 2) + 5 - 4x

Expand 4(x - 2): → 4x - 8

Now plug in:
→ 3 = 4x - 8 + 5 - 4x

Simplify right side: 4x - 4x cancels out → -8 + 5 = -3

So: 3 = -3 → This is FALSE.

Wait — that means no solution? Let’s double-check:

Original: 3 = 4(x - 2) + 5 - 4x
= 4x - 8 + 5 - 4x
= (4x - 4x) + (-8 + 5)
= 0 - 3 = -3

So 3 = -3 → contradiction.

→ No solution

But let me check if I misread... Maybe it's a trick question? Actually, yes — this simplifies to a false statement, so there is no value of x that satisfies it.

Answer: No solution

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Problem 6: (5y)/9 - 3 = 6

Add 3 to both sides:
→ (5y)/9 = 9

Multiply both sides by 9:
→ 5y = 81

Divide by 5:
→ y = 81/5 or 16.2

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Problem 7: n/10 = 9 - n/4

Get all n terms on one side. Add n/4 to both sides:

→ n/10 + n/4 = 9

Find common denominator for fractions: LCD of 10 and 4 is 20.

Convert:
→ (2n)/20 + (5n)/20 = 9
→ (7n)/20 = 9

Multiply both sides by 20:
→ 7n = 180

Divide by 7:
→ n = 180/7 ≈ 25.714...

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Problem 8: 21.1w + 4.6 = 10.9w

Subtract 10.9w from both sides:
→ 10.2w + 4.6 = 0

Subtract 4.6:
→ 10.2w = -4.6

Divide by 10.2:
→ w = -4.6 / 10.2

Simplify: Multiply numerator and denominator by 10 to eliminate decimals:
→ -46 / 102

Reduce fraction: divide numerator and denominator by 2:
→ -23/51

Or as decimal: ≈ -0.45098...

We can leave as fraction unless told otherwise.

→ w = -23/51

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Problem 9: -5(3 - 4x) = -6 + 20x

Left side: distribute -5:
→ -15 + 20x = -6 + 20x

Subtract 20x from both sides:
→ -15 = -6 → FALSE again!

So same as problem 5 — contradiction.

→ No solution

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Problem 10: 9.2z - 4.3 = 50.8

Add 4.3 to both sides:
→ 9.2z = 55.1

Divide by 9.2:
→ z = 55.1 ÷ 9.2

Let’s compute:

9.2 × 6 = 55.2 → too big
9.2 × 5.9 = 9.2×5 + 9.2×0.9 = 46 + 8.28 = 54.28
55.1 - 54.28 = 0.82
0.82 / 9.2 = 0.089... → approx 5.989...

Better to do exact division:

55.1 ÷ 9.2 = 551 ÷ 92 (multiply num and den by 10)

Divide 551 by 92:

92 × 5 = 460
551 - 460 = 91
So 5 + 91/92 → z = 551/92

Check if reducible: 551 ÷ 19 = 29, 92 ÷ 19? No. 551 ÷ 29 = 19, 92 not divisible by 29. So fraction is simplified.

Alternatively, decimal: 551 ÷ 92 = 5.98913...

But since original numbers had 1 decimal, maybe keep as decimal?

Actually, 55.1 / 9.2 = ?

Do 5510 ÷ 920 = same thing.

Use calculator-style: 55.1 ÷ 9.2 = 5.98913043478...

But perhaps we should write exact fraction.

Wait — 55.1 = 551/10, 9.2 = 92/10 → so (551/10)/(92/10) = 551/92

Yes.

Can we reduce 551/92?

Factors of 92: 2×2×23
551 ÷ 23 = 23.956… no
551 ÷ 2 = no
So z = 551/92

But let me verify with decimal:

9.2 × 5.98913 ≈ 9.2 × 6 = 55.2 minus 9.2×0.01087≈0.1 → 55.1 → correct.

But for exactness, better to use fraction.

However, looking back at problem — maybe they expect decimal?

Actually, 55.1 ÷ 9.2:

Multiply numerator and denominator by 10: 551 ÷ 92

Do long division:

92 into 551:

92 × 5 = 460 → subtract → 91
Bring down 0 → 910
92 × 9 = 828 → subtract → 82
Bring down 0 → 820
92 × 8 = 736 → subtract → 84
etc.

So 5.989... but perhaps round?

Wait — actually, 55.1 / 9.2 = ?

Note: 9.2 × 6 = 55.2 → which is 0.1 more than 55.1 → so 6 - (0.1/9.2) = 6 - 1/92 = (552 - 1)/92 = 551/92 → same.

So final answer: z = 551/92

But let me see if it reduces — GCD of 551 and 92.

92 factors: 2² × 23
551 ÷ 23 = 23.956… not integer
551 ÷ 2 = no
So yes, 551/92 is simplest form.

Alternatively, mixed number: 551 ÷ 92 = 5 with remainder 91 → 5 91/92

But probably improper fraction is fine.

Wait — let me check calculation again:

Equation: 9.2z - 4.3 = 50.8
Add 4.3: 9.2z = 55.1
z = 55.1 / 9.2

Now, 55.1 ÷ 9.2 = ?

Let me compute numerically:

9.2 × 5.9 = 9.2×5 + 9.2×0.9 = 46 + 8.28 = 54.28
55.1 - 54.28 = 0.82
0.82 / 9.2 = 82/920 = 41/460 ≈ 0.08913

So total z ≈ 5.98913

But for exact answer, z = 551/92

I think that’s acceptable.

Alternatively, maybe the problem expects decimal rounded? But since others are fractions, I'll go with fraction.

Wait — problem 4 had decimals and we got integer 120. Problem 8 had decimals and we got fraction.

So for consistency, I’ll use fraction here too.

But 551/92 can be written as decimal if needed, but I think fraction is precise.

Actually, let me confirm with another way:

55.1 / 9.2 = 551/92 = ?

Divide 551 by 92:

92 * 5 = 460
551 - 460 = 91 → so 5 and 91/92 → 5 91/92

But in boxed answer, usually improper fraction or decimal.

Looking at other answers, some are fractions, some integers.

For this, I’ll put z = 551/92

But let me see if it simplifies — no, as above.

Alternatively, perhaps I made a mistake in addition?

50.8 + 4.3 = 55.1 — yes.

9.2z = 55.1 — yes.

So z = 55.1 / 9.2

To avoid fraction, multiply numerator and denominator by 10: 551/92 — same.

I think it's fine.

But wait — 551 ÷ 92 = 5.98913043478... and 9.2 * 5.98913043478 = let's compute:

9.2 * 5 = 46
9.2 * 0.98913043478 ≈ 9.2 * 0.99 = 9.108, minus 9.2*0.00086956522≈0.008, so ≈9.1 — total 46+9.1=55.1 — yes.

So correct.

Final Answer for 10: z = 551/92

But perhaps they want decimal? The problem has decimals, so maybe.

In many worksheets, they expect decimal if input is decimal.

Let me calculate exactly:

55.1 ÷ 9.2 = 551 ÷ 92 = 5.989130434782608...

But that's messy. Perhaps leave as fraction.

I recall that 55.1 / 9.2 = 551/92, and it doesn't simplify, so I'll box that.

But let me check online or think — actually, in context, perhaps write as mixed number or decimal.

Since the instruction is to solve accurately, and fraction is exact, I'll use fraction.

But for student-friendly, maybe decimal rounded to two places? But not specified.

Looking at problem 4, we had 0.25 etc., and got integer 120.

Here, it's not integer.

Perhaps I can write it as 5.99 if rounded, but better exact.

Another thought: 55.1 / 9.2 = 551/92 = reduce by dividing by... gcd is 1, as established.

So I'll go with z = \frac{551}{92}

But in the final answer list, I need to present clearly.

Perhaps for this worksheet, they expect decimal.

Let me calculate numerically: 55.1 ÷ 9.2.

Do 5510 ÷ 920 = 551 ÷ 92 same.

92 * 5.989 = 92*5 = 460, 92*0.9=82.8, total 542.8, then 92*0.089= approximately 8.188, total 542.8+8.188=550.988, close to 551.

So 5.989 is good, but for exact, fraction.

I think for accuracy, I'll use the fraction.

But let's see the other problems — problem 6 was 81/5, which is 16.2, so they accept fractions.

Similarly, problem 7 is 180/7.

So for consistency, z = 551/92

Okay.

Now, compiling all answers:

1. x = 5
2. x = 4/3
3. x = -6/7
4. x = 120
5. No solution
6. y = 81/5
7. n = 180/7
8. w = -23/51
9. No solution
10. z = 551/92

For problem 5 and 9, "no solution" is the answer.

Now, for final answer section, I need to list them.

The user didn't specify format, but since it's a worksheet, probably list each answer.

In the response, I'll write the final answers clearly.

Also, for problem 10, I could write it as a decimal, but I think fraction is better.

551/92 can be simplified? 551 and 92.

92 = 4*23
551 ÷ 23 = 23.956 — not integer. 23*23=529, 551-529=22, not divisible. So yes, 551/92 is reduced.

So I'll proceed.

Final Answer:

1. 5
2. \frac{4}{3}
3. -\frac{6}{7}
4. 120
5. No solution
6. \frac{81}{5}
7. \frac{180}{7}
8. -\frac{23}{51}
9. No solution
10. \frac{551}{92}

For problem 10, if they prefer decimal, but I think this is fine.

To match the style, perhaps write as decimals where appropriate, but since others are fractions, keep consistent.

Problem 4 was decimal inputs but integer output.

Here, output is fractional.

I think it's okay.

So now, for the response, since ExplainAnswer is false, I don't need explanation, just final answer.

The user said: "If you're solving math or logic problems, verify your answer before writing it in the Final Answer section."

I have verified each step.

Also, for problem 5 and 9, I confirmed they lead to contradictions.

So ready.

Final Answer:
[Provide only the final correct answer — this should come AFTER all explanations and reasoning.]

But since ExplainAnswer is false, I skip explanation, and go straight to final answer.

The format says: if option is false, omit that section.

So I should only have Final Answer section.

But in the thinking, I did the work.

So in response, I'll write:

Final Answer:
1. \( 5 \)
2. \( \frac{4}{3} \)
3. \( -\frac{6}{7} \)
4. \( 120 \)
5. No solution
6. \( \frac{81}{5} \)
7. \( \frac{180}{7} \)
8. \( -\frac{23}{51} \)
9. No solution
10. \( \frac{551}{92} \)

For problem 10, I recall that 551/92 can be written as 5.989..., but I think fraction is precise.

Perhaps simplify 551/92 — but it's already simplified.

Another way: 551 ÷ 92 = 5.98913043478, but not nice.

I think it's fine.

So I'll box that.

In the final answer, I need to present it neatly.

Since it's a list, I can write:

The solutions are:
1. \( x = 5 \)
2. \( x = \frac{4}{3} \)
3. \( x = -\frac{6}{7} \)
4. \( x = 120 \)
5. No solution
6. \( y = \frac{81}{5} \)
7. \( n = \frac{180}{7} \)
8. \( w = -\frac{23}{51} \)
9. No solution
10. \( z = \frac{551}{92} \)

But the instruction says "provide only the final correct answer", and in the format, it might be expected to list the values.

To be safe, I'll list the answers corresponding to each problem number.

So:

Final Answer:
1. 5
2. \frac{4}{3}
3. -\frac{6}{7}
4. 120
5. No solution
6. \frac{81}{5}
7. \frac{180}{7}
8. -\frac{23}{51}
9. No solution
10. \frac{551}{92}

Yes.

For problem 10, I can write it as a mixed number, but improper fraction is standard.

I think this is correct.