Two-Step Equation Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Two-Step Equations (Decimals)" with several algebraic equations to solve. Since I can't view images directly, I’ll assume you're asking me to solve the problems listed on the worksheet based on the text you provided.

Let’s go through each problem one by one and solve them step-by-step. Here are the equations:

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1. $ 0.6n - 2.3 = 3.5 $

Step 1: Add 2.3 to both sides
$$
0.6n = 3.5 + 2.3 = 5.8
$$

Step 2: Divide both sides by 0.6
$$
n = \frac{5.8}{0.6} = \frac{58}{6} = 9.\overline{6} \approx 9.67
$$

✔ Answer: $ n = 9.\overline{6} $ or $ \boxed{9.67} $

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2. $ \frac{2}{5}x - 3.1 = 7.4 $

Step 1: Add 3.1 to both sides
$$
\frac{2}{5}x = 7.4 + 3.1 = 10.5
$$

Step 2: Multiply both sides by the reciprocal of $ \frac{2}{5} $, which is $ \frac{5}{2} $
$$
x = 10.5 \times \frac{5}{2} = \frac{10.5 \times 5}{2} = \frac{52.5}{2} = 26.25
$$

✔ Answer: $ x = \boxed{26.25} $

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3. $ y - \frac{13}{10} = \frac{3}{2} $

Convert fractions to decimals:
$ \frac{13}{10} = 1.3 $, $ \frac{3}{2} = 1.5 $

Step 1: Add 1.3 to both sides
$$
y = 1.5 + 1.3 = 2.8
$$

✔ Answer: $ y = \boxed{2.8} $

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4. $ 1.7q + 1.55 = -11.5 $

Step 1: Subtract 1.55 from both sides
$$
1.7q = -11.5 - 1.55 = -13.05
$$

Step 2: Divide by 1.7
$$
q = \frac{-13.05}{1.7} = -7.676... \approx -7.68
$$

✔ Answer: $ q = \boxed{-7.68} $ (rounded to two decimal places)

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5. $ -6.8p + 3.2 = -1.2p $

Step 1: Move all terms with $ p $ to one side
Add $ 6.8p $ to both sides:
$$
3.2 = -1.2p + 6.8p = 5.6p
$$

Step 2: Divide by 5.6
$$
p = \frac{3.2}{5.6} = \frac{32}{56} = \frac{4}{7} \approx 0.571
$$

✔ Answer: $ p = \boxed{\frac{4}{7}} $ or $ \boxed{0.57} $

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6. $ -1.6s - 3.4 = -2.5 $

Step 1: Add 3.4 to both sides
$$
-1.6s = -2.5 + 3.4 = 0.9
$$

Step 2: Divide by -1.6
$$
s = \frac{0.9}{-1.6} = -0.5625
$$

✔ Answer: $ s = \boxed{-0.56} $ (rounded to two decimal places)

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7. $ 14.2 - 2.1z = 5.8z - 1 $

Step 1: Move all $ z $-terms to one side and constants to the other
Add $ 2.1z $ to both sides:
$$
14.2 = 5.8z + 2.1z - 1 = 7.9z - 1
$$

Add 1 to both sides:
$$
15.2 = 7.9z
$$

Step 2: Divide by 7.9
$$
z = \frac{15.2}{7.9} \approx 1.924
$$

✔ Answer: $ z = \boxed{1.92} $ (rounded to two decimal places)

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8. $ 10.8 = \frac{10.5 + 1.2}{2.1} $

Wait — this appears to be an equation, but let's check if it's correct.

Left side: $ 10.8 $
Right side: $ \frac{10.5 + 1.2}{2.1} = \frac{11.7}{2.1} \approx 5.57 $

But $ 10.8 \ne 5.57 $, so this is not an equation to solve for a variable — maybe it's a typo?

Alternatively, perhaps it's meant to be:

> Solve: $ 10.8 = \frac{10.5 + 1.2x}{2.1} $ ?

But as written, it's just a false statement.

Assuming it's not a typo and just wants verification, then:

✘ This is not true — $ 10.8 \ne \frac{11.7}{2.1} $. So unless there's a variable missing, this may be incorrect.

But if we assume the intended problem was:

> $ 10.8 = \frac{10.5 + 1.2x}{2.1} $

Then we can solve it.

Step 1: Multiply both sides by 2.1
$$
10.8 \times 2.1 = 10.5 + 1.2x \\
22.68 = 10.5 + 1.2x
$$

Step 2: Subtract 10.5
$$
12.18 = 1.2x
$$

Step 3: Divide by 1.2
$$
x = \frac{12.18}{1.2} = 10.15
$$

✔ If that’s the intended problem: $ x = \boxed{10.15} $

But since the original says "10.8 = (10.5 + 1.2)/2.1", it's likely a mistake.

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9. $ \frac{5}{6}r + 7.8 = 0 $

Step 1: Subtract 7.8
$$
\frac{5}{6}r = -7.8
$$

Step 2: Multiply both sides by $ \frac{6}{5} $
$$
r = -7.8 \times \frac{6}{5} = -\frac{7.8 \times 6}{5} = -\frac{46.8}{5} = -9.36
$$

✔ Answer: $ r = \boxed{-9.36} $

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10. $ -5.1 = 2v - 6.3 $

Step 1: Add 6.3 to both sides
$$
-5.1 + 6.3 = 2v \Rightarrow 1.2 = 2v
$$

Step 2: Divide by 2
$$
v = \frac{1.2}{2} = 0.6
$$

✔ Answer: $ v = \boxed{0.6} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ n = 9.\overline{6} $ or $ 9.67 $ |
| 2 | $ x = 26.25 $ |
| 3 | $ y = 2.8 $ |
| 4 | $ q = -7.68 $ |
| 5 | $ p = \frac{4}{7} $ or $ 0.57 $ |
| 6 | $ s = -0.56 $ |
| 7 | $ z = 1.92 $ |
| 8 | Likely typo; if $ 10.8 = \frac{10.5 + 1.2x}{2.1} $, then $ x = 10.15 $ |
| 9 | $ r = -9.36 $ |
| 10 | $ v = 0.6 $ |

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If you'd like me to recheck any specific problem or explain a step in more detail, feel free to ask!