Question

how many solutions exist for the given equation?
3(x + 10) + 6 = 3(x + 12)
zero
one
two
infinitely many

Explanation:

Step1: Expand both sides

First, expand the left - hand side: \(3(x + 10)+6=3x+30 + 6=3x+36\)
Then, expand the right - hand side: \(3(x + 12)=3x+36\)

Step2: Analyze the equation

We have the equation \(3x + 36=3x+36\)
Subtract \(3x\) from both sides of the equation: \(3x-3x + 36=3x-3x+36\)
Which simplifies to \(36 = 36\)
This is a true statement for all values of \(x\).

Answer:

infinitely many