Question

which of the following equations has infinitely many real solutions?
a. 5x + 1 = x - 1
b. 5x + 1 = 5x - 1
c. 5(x - 8) = 5x - 40

Explanation:

Step1: Analyze Option A

Solve \(5x + 1 = x - 1\). Subtract \(x\) from both sides: \(4x+1=-1\). Subtract 1: \(4x=-2\), so \(x = -\frac{1}{2}\). One solution.

Step2: Analyze Option B

Solve \(5x + 1 = 5x - 1\). Subtract \(5x\): \(1=-1\), which is false. No solution.

Step3: Analyze Option C

Simplify \(5(x - 8)=5x - 40\). Distribute left side: \(5x-40 = 5x - 40\). Subtract \(5x\): \(-40=-40\), always true. Infinitely many solutions.

Answer:

C. \(5(x - 8) = 5x - 40\)