Which of the following equations have a solution of z = 3 ?

Question

​
​Select the TWO correct equations.
Responses

9z − 5 = 22
9z − 5 = 22

5z + 40 = 62
5z + 40 = 62

9z + 22 = 26
9z + 22 = 26

54 − 8z = 30

Answer 1

To determine which of the given equations have a solution of \( z = 3 \), we will substitute \( z = 3 \) into each equation and check if both sides are equal.

1. For the equation \( 9z - 5 = 22 \): \[ 9(3) - 5 = 27 - 5 = 22 \quad \text{(True, so this equation is correct)} \]

2. For the equation \( 5z + 40 = 62 \): \[ 5(3) + 40 = 15 + 40 = 55 \quad \text{(False, so this equation is not correct)} \]

3. For the equation \( 9z + 22 = 26 \): \[ 9(3) + 22 = 27 + 22 = 49 \quad \text{(False, so this equation is not correct)} \]

4. For the equation \( 54 - 8z = 30 \): \[ 54 - 8(3) = 54 - 24 = 30 \quad \text{(True, so this equation is correct)} \]

The equations that have a solution of \( z = 3 \) are:

• \( 9z - 5 = 22 \)
• \( 54 - 8z = 30 \)

So the correct responses are:

1. \( 9z - 5 = 22 \)
2. \( 54 - 8z = 30 \)