Two Step Equations Worksheets - Math Monks - Free Printable

Let’s solve each equation step by step. We’ll isolate the variable (the letter) on one side of the equation using inverse operations — that means undoing what’s being done to the variable, in reverse order.

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Problem ①:
$\frac{x}{6} - 3 = -11$

Step 1: Add 3 to both sides to undo the subtraction.
$\frac{x}{6} = -8$

Step 2: Multiply both sides by 6 to undo the division.
$x = -48$

✔ Check: $\frac{-48}{6} - 3 = -8 - 3 = -11$ → Correct!

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Problem ②:
$\frac{1}{4}(8x + 12) = 7$

Step 1: Multiply both sides by 4 to undo the fraction.
$8x + 12 = 28$

Step 2: Subtract 12 from both sides.
$8x = 16$

Step 3: Divide both sides by 8.
$x = 2$

✔ Check: $\frac{1}{4}(8*2 + 12) = \frac{1}{4}(16+12) = \frac{28}{4} = 7$ → Correct!

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Problem ③:
$1 - \frac{d}{4} = -7$

Step 1: Subtract 1 from both sides.
$-\frac{d}{4} = -8$

Step 2: Multiply both sides by -4 to solve for d.
$d = 32$

✔ Check: $1 - \frac{32}{4} = 1 - 8 = -7$ → Correct!

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Problem ④:
$42 + 5s = 8s$

Step 1: Subtract 5s from both sides to get all s terms on one side.
$42 = 3s$

Step 2: Divide both sides by 3.
$s = 14$

✔ Check: $42 + 5*14 = 42 + 70 = 112$, and $8*14 = 112$ → Correct!

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Problem ⑤:
$\frac{m}{4} - 9 = -5$

Step 1: Add 9 to both sides.
$\frac{m}{4} = 4$

Step 2: Multiply both sides by 4.
$m = 16$

✔ Check: $\frac{16}{4} - 9 = 4 - 9 = -5$ → Correct!

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Problem ⑥:
$3(n + 5) = -5$

Step 1: Divide both sides by 3.
$n + 5 = -\frac{5}{3}$

Step 2: Subtract 5 from both sides.
$n = -\frac{5}{3} - 5 = -\frac{5}{3} - \frac{15}{3} = -\frac{20}{3}$

✔ Check: $3(-\frac{20}{3} + 5) = 3(-\frac{20}{3} + \frac{15}{3}) = 3(-\frac{5}{3}) = -5$ → Correct!

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Problem ⑦:
$\frac{y - 3}{6} = 9$

Step 1: Multiply both sides by 6.
$y - 3 = 54$

Step 2: Add 3 to both sides.
$y = 57$

✔ Check: $\frac{57 - 3}{6} = \frac{54}{6} = 9$ → Correct!

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Problem ⑧:
$-1 = \frac{5 + v}{6}$

Step 1: Multiply both sides by 6.
$-6 = 5 + v$

Step 2: Subtract 5 from both sides.
$v = -11$

✔ Check: $\frac{5 + (-11)}{6} = \frac{-6}{6} = -1$ → Correct!

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Problem ⑨:
$\frac{p + 3}{2} = 7.5$

Step 1: Multiply both sides by 2.
$p + 3 = 15$

Step 2: Subtract 3 from both sides.
$p = 12$

✔ Check: $\frac{12 + 3}{2} = \frac{15}{2} = 7.5$ → Correct!

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Problem ⑩:
$-2 = 2 + \frac{p}{4}$

Step 1: Subtract 2 from both sides.
$-4 = \frac{p}{4}$

Step 2: Multiply both sides by 4.
$p = -16$

✔ Check: $2 + \frac{-16}{4} = 2 - 4 = -2$ → Correct!

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Final Answer:
① x = -48
② x = 2
③ d = 32
④ s = 14
⑤ m = 16
⑥ n = -20/3
⑦ y = 57
⑧ v = -11
⑨ p = 12
⑩ p = -16