Grade 5 Pre-Algebra worksheet focusing on solving 2-step equations.

Let's solve each of these two-step equations step by step. The goal is to isolate the variable (usually *x* or *y*) on one side of the equation.

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1) 10x − 76 = 754

Step 1: Add 76 to both sides
10x = 754 + 76
10x = 830

Step 2: Divide both sides by 10
x = 830 ÷ 10
x = 83

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2) 14y − 19 = 499

Step 1: Add 19 to both sides
14y = 499 + 19
14y = 518

Step 2: Divide both sides by 14
y = 518 ÷ 14
y = 37

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3) 11 + 55y = 2,981

Step 1: Subtract 11 from both sides
55y = 2,981 − 11
55y = 2,970

Step 2: Divide both sides by 55
y = 2,970 ÷ 55
y = 54

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4) 10z − 46 = 4

Step 1: Add 46 to both sides
10z = 4 + 46
10z = 50

Step 2: Divide both sides by 10
z = 50 ÷ 10
z = 5

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5) 40x + 42 = 1,162

Step 1: Subtract 42 from both sides
40x = 1,162 − 42
40x = 1,120

Step 2: Divide both sides by 40
x = 1,120 ÷ 40
x = 28

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6) 73 + 15x = 343

Step 1: Subtract 73 from both sides
15x = 343 − 73
15x = 270

Step 2: Divide both sides by 15
x = 270 ÷ 15
x = 18

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7) 2,528 − 72y = 8

Step 1: Subtract 2,528 from both sides
−72y = 8 − 2,528
−72y = −2,520

Step 2: Divide both sides by −72
y = (−2,520) ÷ (−72)
y = 35

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8) 81 + 68x = 1,849

Step 1: Subtract 81 from both sides
68x = 1,849 − 81
68x = 1,768

Step 2: Divide both sides by 68
x = 1,768 ÷ 68
x = 26

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9) 72y − 93 = 5,367

Step 1: Add 93 to both sides
72y = 5,367 + 93
72y = 5,460

Step 2: Divide both sides by 72
y = 5,460 ÷ 72
y = 75.833... → Wait! Let's check:

Actually:
5,460 ÷ 72 = ?

Let’s divide:
72 × 75 = 5,400
5,460 − 5,400 = 60
So, 75 + 60/72 = 75 + 5/6 ≈ 75.833...

But let's see if it divides evenly:

Wait — maybe I made a mistake. Let's do it carefully:

72 × 75 = 5,400
5,460 − 5,400 = 60
60 ÷ 72 = 5/6 → not a whole number?

But let's double-check original equation:

72y − 93 = 5,367
72y = 5,367 + 93 = 5,460
Now: 5,460 ÷ 72

Divide numerator and denominator by 12:
5,460 ÷ 12 = 455
72 ÷ 12 = 6
So: 455 ÷ 6 = 75.833... → Not a whole number?

Wait — perhaps there's a typo or we should keep as fraction.

But let's check:
72 × 75 = 5,400
72 × 76 = 5,472 → too big
So no integer solution. But maybe it's okay.

Wait — let me recalculate:
Is 5,460 divisible by 72?

72 × 75 = 5,400
5,460 − 5,400 = 60 → remainder 60

So y = 5,460 / 72 = 455 / 6 = 75.833...

But let's simplify:

5,460 ÷ 72 = (divide numerator and denominator by 12):
5,460 ÷ 12 = 455
72 ÷ 12 = 6
So 455/6 = 75 5/6

But since this is a pre-algebra worksheet, maybe it's supposed to be an integer.

Wait — did I add correctly?

72y = 5,367 + 93 = 5,460 → correct

Try dividing 5,460 ÷ 72:

Do long division:

72 into 546 → 7 times (7×72=504), subtract: 546−504=42
Bring down 0 → 420
72 into 420 → 5 times (5×72=360), remainder 60
So 75.833... → y = 75.833..., or 75 5/6

But let’s assume decimal is acceptable.

y ≈ 75.83

Wait — maybe I made a calculation error earlier?

Wait — let's try plugging back in:

72 × 75.833... = 72 × (75 + 5/6) = 72×75 + 72×(5/6) = 5,400 + 60 = 5,460 → yes.

So y = 5,460 / 72 = 455 / 6 = 75 5/6

But perhaps better to leave as improper fraction or decimal.

But let's move on and come back.

Wait — maybe the problem expects exact fraction.

So y = 455/6 or 75 5/6

But let's check if I copied the problem right:
"72y − 93 = 5,367"

Yes.

So y = 5,460 / 72 = 75.833...

We'll write it as y = 75.83 (approx), but better to simplify:

5,460 ÷ 72 = divide numerator and denominator by 12:
5,460 ÷ 12 = 455
72 ÷ 12 = 6 → so y = 455/6

So y = 455/6 or 75 5/6

But let's keep it as y = 75.83 for now.

Wait — actually, let's check again:
72 × 75 = 5,400
72 × 76 = 5,472 → too big
So no, not integer.

So y = 5,460 / 72 = 75.833...

But let's reduce:
GCF of 5460 and 72?

72 = 8×9 = 2³×3²
5460 ÷ 2 = 2730; ÷2=1365 → odd
So divisible by 4? 5460 ÷ 4 = 1365 → yes
5460 ÷ 4 = 1365
72 ÷ 4 = 18 → 1365 / 18

1365 ÷ 3 = 455
18 ÷ 3 = 6 → 455 / 6

So y = 455/6 → final answer.

y = 455/6 or 75 5/6

We’ll write it as y = 75.83 if decimal, but exact is 455/6

But let's keep going.

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10) 57z + 93 = 435

Step 1: Subtract 93 from both sides
57z = 435 − 93
57z = 342

Step 2: Divide both sides by 57
z = 342 ÷ 57
Let’s compute:
57 × 6 = 342 → so z = 6

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11) 13 + 33y = 277

Step 1: Subtract 13 from both sides
33y = 277 − 13
33y = 264

Step 2: Divide both sides by 33
y = 264 ÷ 33
33 × 8 = 264 → so y = 8

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12) 77 + 82x = 7,867

Step 1: Subtract 77 from both sides
82x = 7,867 − 77
82x = 7,790

Step 2: Divide both sides by 82
x = 7,790 ÷ 82

Let’s divide:

82 × 90 = 7,380
7,790 − 7,380 = 410
82 × 5 = 410 → so total = 90 + 5 = 95

Check: 82 × 95 = ?

82 × 90 = 7,380
82 × 5 = 410
Total = 7,380 + 410 = 7,790 → yes!

So x = 95

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✔ Final Answers:

1) x = 83
2) y = 37
3) y = 54
4) z = 5
5) x = 28
6) x = 18
7) y = 35
8) x = 26
9) y = 455/6 or 75 5/6 (or 75.83)
10) z = 6
11) y = 8
12) x = 95

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Notes:

- For #9, the answer is not an integer, but that’s okay. It’s still correct.
- Always check your work by plugging back in.

Would you like me to show the verification for any of them?