Seventh Grade Two-Step Equations Activity (teacher made) - Free Printable

Problem: Solve the Two-Step Equations and Answer the Word Problems

The image contains a worksheet titled "Two-Step Equations." Below is a detailed solution for each problem, step by step.

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#### Section 1: Solve Each Equation

1. Equation: \( 18 - x = 5 \)
- Step 1: Isolate the variable \( x \). To do this, subtract 18 from both sides of the equation:
\[
18 - x - 18 = 5 - 18
\]
\[
-x = -13
\]
- Step 2: Multiply both sides by \(-1\) to solve for \( x \):
\[
x = 13
\]
- Answer: \( x = 13 \)

2. Equation: \( 12z = 2z + 6 \)
- Step 1: Subtract \( 2z \) from both sides to isolate the term with \( z \):
\[
12z - 2z = 2z + 6 - 2z
\]
\[
10z = 6
\]
- Step 2: Divide both sides by 10 to solve for \( z \):
\[
z = \frac{6}{10} = \frac{3}{5}
\]
- Answer: \( z = \frac{3}{5} \)

3. Equation: \( \frac{r}{6} + 11 = 14 \)
- Step 1: Subtract 11 from both sides to isolate the fraction:
\[
\frac{r}{6} + 11 - 11 = 14 - 11
\]
\[
\frac{r}{6} = 3
\]
- Step 2: Multiply both sides by 6 to solve for \( r \):
\[
r = 3 \times 6 = 18
\]
- Answer: \( r = 18 \)

4. Equation: \( 3m - 1 = 20 \)
- Step 1: Add 1 to both sides to isolate the term with \( m \):
\[
3m - 1 + 1 = 20 + 1
\]
\[
3m = 21
\]
- Step 2: Divide both sides by 3 to solve for \( m \):
\[
m = \frac{21}{3} = 7
\]
- Answer: \( m = 7 \)

5. Equation: \( 9y + 7 = 52 \)
- Step 1: Subtract 7 from both sides to isolate the term with \( y \):
\[
9y + 7 - 7 = 52 - 7
\]
\[
9y = 45
\]
- Step 2: Divide both sides by 9 to solve for \( y \):
\[
y = \frac{45}{9} = 5
\]
- Answer: \( y = 5 \)

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#### Section 2: Write and Solve the Equation for Each Scenario

6. Scenario: The sum of three consecutive numbers is 27. What is the smallest of these numbers?
- Step 1: Let the three consecutive numbers be \( x \), \( x + 1 \), and \( x + 2 \). Their sum is given as 27:
\[
x + (x + 1) + (x + 2) = 27
\]
- Step 2: Simplify the equation:
\[
x + x + 1 + x + 2 = 27
\]
\[
3x + 3 = 27
\]
- Step 3: Subtract 3 from both sides:
\[
3x + 3 - 3 = 27 - 3
\]
\[
3x = 24
\]
- Step 4: Divide both sides by 3:
\[
x = \frac{24}{3} = 8
\]
- Answer: The smallest number is \( x = 8 \).

7. Scenario: The aquarium had 24 species of fish. They returned some of their habitat and only had 17 left in the aquarium. How many were returned to their natural habitat?
- Step 1: Let the number of fish returned be \( r \). The total number of fish initially was 24, and after returning some, 17 remained:
\[
24 - r = 17
\]
- Step 2: Solve for \( r \) by subtracting 17 from 24:
\[
r = 24 - 17 = 7
\]
- Answer: The number of fish returned is \( r = 7 \).

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Final Answers:

1. \( x = 13 \)
2. \( z = \frac{3}{5} \)
3. \( r = 18 \)
4. \( m = 7 \)
5. \( y = 5 \)
6. The smallest number is \( 8 \).
7. The number of fish returned is \( 7 \).

\[
\boxed{13, \frac{3}{5}, 18, 7, 5, 8, 7}
\]