Two-Step Equation Worksheets (printable, online, answers, examples) - Free Printable

Let’s solve each equation step by step. Remember, we want to get the variable (x) alone on one side of the equation. We do this by undoing what’s being done to x — first addition/subtraction, then multiplication/division.

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Equation 1:
\[
\frac{3}{4}x + 6 = 15
\]

Step 1: Subtract 6 from both sides.
\[
\frac{3}{4}x = 9
\]

Step 2: Multiply both sides by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\).
\[
x = 9 \cdot \frac{4}{3} = \frac{36}{3} = 12
\]

✔ Answer: \(x = 12\)

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Equation 2:
\[
\frac{2}{3}x - 4 = 1
\]

Step 1: Add 4 to both sides.
\[
\frac{2}{3}x = 5
\]

Step 2: Multiply both sides by \(\frac{3}{2}\).
\[
x = 5 \cdot \frac{3}{2} = \frac{15}{2} = 7.5
\]

✔ Answer: \(x = 7.5\) or \(\frac{15}{2}\)

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Equation 3:
\[
\frac{5}{6}x - 10 = 5
\]

Step 1: Add 10 to both sides.
\[
\frac{5}{6}x = 15
\]

Step 2: Multiply both sides by \(\frac{6}{5}\).
\[
x = 15 \cdot \frac{6}{5} = \frac{90}{5} = 18
\]

✔ Answer: \(x = 18\)

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Equation 4:
\[
10 = \frac{2}{5}x - 8
\]

Step 1: Add 8 to both sides.
\[
18 = \frac{2}{5}x
\]

Step 2: Multiply both sides by \(\frac{5}{2}\).
\[
x = 18 \cdot \frac{5}{2} = \frac{90}{2} = 45
\]

✔ Answer: \(x = 45\)

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Equation 5:
\[
\frac{4}{5}x - 2 = 2
\]

Step 1: Add 2 to both sides.
\[
\frac{4}{5}x = 4
\]

Step 2: Multiply both sides by \(\frac{5}{4}\).
\[
x = 4 \cdot \frac{5}{4} = 5
\]

✔ Answer: \(x = 5\)

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Equation 6:
\[
6 = \frac{2}{3}x - 3
\]

Step 1: Add 3 to both sides.
\[
9 = \frac{2}{3}x
\]

Step 2: Multiply both sides by \(\frac{3}{2}\).
\[
x = 9 \cdot \frac{3}{2} = \frac{27}{2} = 13.5
\]

✔ Answer: \(x = 13.5\) or \(\frac{27}{2}\)

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Equation 7:
\[
6 + \frac{7}{2}x = 13
\]

Step 1: Subtract 6 from both sides.
\[
\frac{7}{2}x = 7
\]

Step 2: Multiply both sides by \(\frac{2}{7}\).
\[
x = 7 \cdot \frac{2}{7} = 2
\]

✔ Answer: \(x = 2\)

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Equation 8:
\[
\frac{7}{8}x - 6 = 8
\]

Step 1: Add 6 to both sides.
\[
\frac{7}{8}x = 14
\]

Step 2: Multiply both sides by \(\frac{8}{7}\).
\[
x = 14 \cdot \frac{8}{7} = \frac{112}{7} = 16
\]

✔ Answer: \(x = 16\)

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Final Answer:
- Equation 1: \(x = 12\)
- Equation 2: \(x = 7.5\) or \(\frac{15}{2}\)
- Equation 3: \(x = 18\)
- Equation 4: \(x = 45\)
- Equation 5: \(x = 5\)
- Equation 6: \(x = 13.5\) or \(\frac{27}{2}\)
- Equation 7: \(x = 2\)
- Equation 8: \(x = 16\)