Grade 9 Mathematics worksheet on solving multi-step equations.

Let's solve each of these multi-step equations step by step.

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1) $ 2a - 6 = 4 $

Step 1: Add 6 to both sides to isolate the term with $ a $:
$$
2a - 6 + 6 = 4 + 6 \\
2a = 10
$$

Step 2: Divide both sides by 2:
$$
a = \frac{10}{2} = 5
$$

✔ Answer: $ a = 5 $

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2) $ \frac{n+1}{-2} = 15 $

Step 1: Multiply both sides by $-2$ to eliminate the denominator:
$$
n + 1 = 15 \times (-2) \\
n + 1 = -30
$$

Step 2: Subtract 1 from both sides:
$$
n = -30 - 1 = -31
$$

✔ Answer: $ n = -31 $

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3) $ 9x + 27 = -72 $

Step 1: Subtract 27 from both sides:
$$
9x = -72 - 27 \\
9x = -99
$$

Step 2: Divide both sides by 9:
$$
x = \frac{-99}{9} = -11
$$

✔ Answer: $ x = -11 $

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4) $ \frac{y}{5} - 6 = 8 $

Step 1: Add 6 to both sides:
$$
\frac{y}{5} = 8 + 6 \\
\frac{y}{5} = 14
$$

Step 2: Multiply both sides by 5:
$$
y = 14 \times 5 = 70
$$

✔ Answer: $ y = 70 $

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✔ Final Answers:

1) $ a = 5 $
2) $ n = -31 $
3) $ x = -11 $
4) $ y = 70 $

Let me know if you'd like a visual explanation or practice problems!