Let's carefully solve the equation [tex]\( -2x + 6x - 8 = 12 \)[/tex] step-by-step.
### Step 1: Combine like terms
First, combine the terms that contain [tex]\( x \)[/tex]:
[tex]\[
-2x + 6x - 8 = 12
\][/tex]
Combine [tex]\( -2x \)[/tex] and [tex]\( 6x \)[/tex]:
[tex]\[
(6x - 2x) - 8 = 12
\][/tex]
This simplifies to:
[tex]\[
4x - 8 = 12
\][/tex]
### Step 2: Isolate the term with [tex]\( x \)[/tex]
To isolate the term with [tex]\( x \)[/tex], add 8 to both sides of the equation:
[tex]\[
4x - 8 + 8 = 12 + 8
\][/tex]
This simplifies to:
[tex]\[
4x = 20
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
To solve for [tex]\( x \)[/tex], divide both sides of the equation by 4:
[tex]\[
\frac{4x}{4} = \frac{20}{4}
\][/tex]
This simplifies to:
[tex]\[
x = 5
\][/tex]
So, the solution to the equation [tex]\( -2x + 6x - 8 = 12 \)[/tex] is [tex]\( x = 5 \)[/tex].
