Two-step equations involving decimals worksheet for solving algebraic problems.

Let's solve each of these two-step equations involving decimals step by step.

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1) $-5.6p + 129 = -1.3p$

Step 1: Get all terms with $p$ on one side.
Add $5.6p$ to both sides:

$$
-5.6p + 5.6p + 129 = -1.3p + 5.6p
$$
$$
129 = 4.3p
$$

Step 2: Divide both sides by 4.3:

$$
p = \frac{129}{4.3}
$$

Now divide:

$$
p = 30
$$

✔ Answer: $p = 30$

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2) $-7.7 - n = 1$

Step 1: Add 7.7 to both sides:

$$
-7.7 - n + 7.7 = 1 + 7.7
$$
$$
-n = 8.7
$$

Step 2: Multiply both sides by $-1$:

$$
n = -8.7
$$

✔ Answer: $n = -8.7$

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3) $9.1 = 2y + 3.5$

Step 1: Subtract 3.5 from both sides:

$$
9.1 - 3.5 = 2y
$$
$$
5.6 = 2y
$$

Step 2: Divide by 2:

$$
y = \frac{5.6}{2} = 2.8
$$

✔ Answer: $y = 2.8$

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4) $-6.5 = \frac{d}{0.2} - 12$

Step 1: Add 12 to both sides:

$$
-6.5 + 12 = \frac{d}{0.2}
$$
$$
5.5 = \frac{d}{0.2}
$$

Step 2: Multiply both sides by 0.2:

$$
d = 5.5 \times 0.2 = 1.1
$$

✔ Answer: $d = 1.1$

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5) $\frac{v - 10.9}{5} = -8.4$

Step 1: Multiply both sides by 5:

$$
v - 10.9 = -8.4 \times 5 = -42
$$

Step 2: Add 10.9 to both sides:

$$
v = -42 + 10.9 = -31.1
$$

✔ Answer: $v = -31.1$

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6) $-c - 2.1 = -14.7$

Step 1: Add 2.1 to both sides:

$$
-c = -14.7 + 2.1 = -12.6
$$

Step 2: Multiply both sides by $-1$:

$$
c = 12.6
$$

✔ Answer: $c = 12.6$

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7) $7.3r - 15 = 6.3r$

Step 1: Subtract $6.3r$ from both sides:

$$
7.3r - 6.3r - 15 = 0
$$
$$
r - 15 = 0
$$

Step 2: Add 15 to both sides:

$$
r = 15
$$

✔ Answer: $r = 15$

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8) $3.6 = 1.5(8.8 + x)$

Step 1: Divide both sides by 1.5:

$$
\frac{3.6}{1.5} = 8.8 + x
$$
$$
2.4 = 8.8 + x
$$

Step 2: Subtract 8.8 from both sides:

$$
x = 2.4 - 8.8 = -6.4
$$

✔ Answer: $x = -6.4$

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✔ Final Answers:

1) $p = 30$
2) $n = -8.7$
3) $y = 2.8$
4) $d = 1.1$
5) $v = -31.1$
6) $c = 12.6$
7) $r = 15$
8) $x = -6.4$

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