Certainly! Let's solve the equation [tex]\(3(x - 3) = 9\)[/tex] step-by-step.
1. Distribute the 3 on the left side of the equation:
Start by applying the distributive property to the term [tex]\( 3 \cdot (x - 3) \)[/tex]. This involves multiplying 3 by both [tex]\( x \)[/tex] and [tex]\( -3 \)[/tex]:
[tex]\[
3(x - 3) = 3 \cdot x - 3 \cdot 3 = 3x - 9
\][/tex]
So the equation now looks like:
[tex]\[
3x - 9 = 9
\][/tex]
2. Isolate the term with [tex]\( x \)[/tex]:
In order to isolate the term containing [tex]\( x \)[/tex] on one side of the equation, we need to eliminate the constant term on the same side. To do this, add 9 to both sides of the equation:
[tex]\[
3x - 9 + 9 = 9 + 9
\][/tex]
Simplifying both sides results in:
[tex]\[
3x = 18
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], divide both sides of the equation by 3:
[tex]\[
\frac{3x}{3} = \frac{18}{3}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 6
\][/tex]
Therefore, the solution to the equation [tex]\(3(x - 3) = 9\)[/tex] is [tex]\( x = 6 \)[/tex].
