Question

for each value of x, determine whether it is a solution to -24 = -2(x + 7).
| x | is it a solution?

-2	∘ (yes)	∘ (no, selected)
-4	∘ (yes)	∘ (no)
7	∘ (yes)	∘ (no)
5	∘ (yes)	∘ (no)

Explanation:

Step1: Solve the equation for x

First, solve the equation \(-24 = -2(x + 7)\). Divide both sides by \(-2\):
\(\frac{-24}{-2}=\frac{-2(x + 7)}{-2}\)
\(12 = x + 7\)

Then, subtract 7 from both sides:
\(12 - 7 = x + 7 - 7\)
\(x = 5\)

Step2: Check each value of x

• For \(x = -2\): Substitute into \(-2(x + 7)\): \(-2(-2 + 7)=-2(5)=-10

eq -24\), so not a solution.

• For \(x = -4\): Substitute: \(-2(-4 + 7)=-2(3)=-6

eq -24\), not a solution.

• For \(x = 7\): Substitute: \(-2(7 + 7)=-2(14)=-28

eq -24\), not a solution.

• For \(x = 5\): Substitute: \(-2(5 + 7)=-2(12)=-24\), which matches, so it is a solution.

Answer:

• For \(x = -2\): No
• For \(x = -4\): No
• For \(x = 7\): No
• For \(x = 5\): Yes

(To mark in the table: For \(x = 5\), select "Yes"; for \(x = -2\), \(x = -4\), \(x = 7\), select "No".)