To solve the equation [tex]\( 4(2x - 6) = 10x - 6 \)[/tex] for [tex]\( x \)[/tex], we can follow these steps:
1. Expand and simplify both sides of the equation:
Start by expanding the left-hand side:
[tex]\[
4(2x - 6) = 4 \cdot 2x - 4 \cdot 6 = 8x - 24
\][/tex]
So, the equation becomes:
[tex]\[
8x - 24 = 10x - 6
\][/tex]
2. Rearrange the equation to isolate the variable [tex]\( x \)[/tex]:
Start by getting all the [tex]\( x \)[/tex] terms on one side and the constant terms on the other. We can do this by subtracting [tex]\( 8x \)[/tex] from both sides:
[tex]\[
8x - 24 - 8x = 10x - 6 - 8x
\][/tex]
Simplify:
[tex]\[
-24 = 2x - 6
\][/tex]
Next, add 6 to both sides to move the constants to one side:
[tex]\[
-24 + 6 = 2x - 6 + 6
\][/tex]
This simplifies to:
[tex]\[
-18 = 2x
\][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[
\frac{-18}{2} = \frac{2x}{2}
\][/tex]
Simplify:
[tex]\[
-9 = x
\][/tex]
So, the solution to the equation [tex]\( 4(2x - 6) = 10x - 6 \)[/tex] is [tex]\( x = -9 \)[/tex]. Among the given choices, the correct answer is:
c. -9
