To determine how many solutions the equation [tex]\( 6x + 15 = 6(x - 3) \)[/tex] has, let's solve it step-by-step.
1. Simplify both sides of the equation:
The left side is already simplified:
[tex]\[
6x + 15
\][/tex]
Let's simplify the right side:
[tex]\[
6(x - 3)
\][/tex]
Distribute the 6:
[tex]\[
6x - 18
\][/tex]
2. Rewrite the equation with the simplified expressions:
[tex]\[
6x + 15 = 6x - 18
\][/tex]
3. Eliminate the [tex]\(6x\)[/tex] terms from both sides:
Subtract [tex]\(6x\)[/tex] from both sides of the equation:
[tex]\[
6x + 15 - 6x = 6x - 18 - 6x
\][/tex]
Simplify this:
[tex]\[
15 = -18
\][/tex]
4. Analyze the resulting statement:
The statement [tex]\(15 = -18\)[/tex] is clearly false. There are no values of [tex]\(x\)[/tex] that can make this equation true.
Thus, we conclude that the equation has no solutions. The correct answer is:
[tex]\[
\boxed{0}
\][/tex]
