Question

which equation has an infinite number of solutions?
○ $12 = 3y$
○ $8q + 5 = 21$
○ $2x + 7 - 2x = 7$
○ $4p - 4 = 4p + 4$

Explanation:

Step1: Analyze \(12 = 3y\)

Solve for \(y\): \(y=\frac{12}{3}=4\). Only one solution.

Step2: Analyze \(8q + 5 = 21\)

Subtract 5: \(8q=21 - 5 = 16\), then \(q=\frac{16}{8}=2\). One solution.

Step3: Analyze \(2x + 7 - 2x = 7\)

Simplify left - hand side: \(2x-2x + 7=7\), which is \(7 = 7\). This is always true, so there are infinite solutions.

Step4: Analyze \(4p - 4 = 4p + 4\)

Subtract \(4p\): \(-4=4\), which is false. No solutions.

Answer:

\(2x + 7 - 2x = 7\) (the third equation)