Question

question 7 of 10
how many solutions are there to the equation below?
6x + 15 = 6(x - 3)

a. 0
b. infinitely many
c. 1

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the equation \(6(x - 3)\) using the distributive property \(a(b - c)=ab - ac\). Here, \(a = 6\), \(b=x\) and \(c = 3\), so \(6(x-3)=6x-18\). The equation becomes \(6x + 15=6x-18\).

Step2: Subtract \(6x\) from both sides

Subtract \(6x\) from both sides of the equation \(6x + 15=6x-18\). We get \((6x-6x)+15=(6x - 6x)-18\), which simplifies to \(15=- 18\).

Since \(15=-18\) is a false statement, this means that there are no values of \(x\) that can satisfy the original equation.

Answer:

A. 0