One- & Two-Step Equations

Question

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Question
Which of the following equations has a solution of −7
?(1 point)
Responses

−x+3=−4
negative x plus 3 equals negative 4

5x+11=−24
5 x plus 11 equals negative 24

−3x−8=−29
negative 3 x minus 8 equals negative 29

4x−23=5

Answer 1

To determine which of the given equations has a solution of \( x = -7 \), we can substitute \(-7\) into each equation and see which one holds true.

1. Equation: \(-x + 3 = -4\) \[ -(-7) + 3 = -4 \quad \Rightarrow \quad 7 + 3 = -4 \quad \Rightarrow \quad 10 \neq -4 \quad (\text{False}) \]

2. Equation: \(5x + 11 = -24\) \[ 5(-7) + 11 = -24 \quad \Rightarrow \quad -35 + 11 = -24 \quad \Rightarrow \quad -24 = -24 \quad (\text{True}) \]

3. Equation: \(-3x - 8 = -29\) \[ -3(-7) - 8 = -29 \quad \Rightarrow \quad 21 - 8 = -29 \quad \Rightarrow \quad 13 \neq -29 \quad (\text{False}) \]

4. Equation: \(4x - 23 = 5\) \[ 4(-7) - 23 = 5 \quad \Rightarrow \quad -28 - 23 = 5 \quad \Rightarrow \quad -51 \neq 5 \quad (\text{False}) \]

From this, we see that the only equation for which \( x = -7 \) is a solution is the second one:

Answer: \(5x + 11 = -24\).