Sure! Let's solve the equation step-by-step.
We are given the equation:
[tex]\[ 2x - 2^2 = 4x + 8 \][/tex]
1. Simplify the exponentiation on the left-hand side:
[tex]\[ 2x - 4 = 4x + 8 \][/tex]
2. To isolate [tex]\( x \)[/tex], let's first get all the [tex]\( x \)[/tex]-terms on one side and the constant terms on the other side. Subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[ 2x - 4 - 2x = 4x + 8 - 2x \][/tex]
This simplifies to:
[tex]\[ -4 = 2x + 8 \][/tex]
3. Now, subtract 8 from both sides to isolate the term involving [tex]\( x \)[/tex] on one side:
[tex]\[ -4 - 8 = 2x + 8 - 8 \][/tex]
This simplifies to:
[tex]\[ -12 = 2x \][/tex]
4. Finally, to solve for [tex]\( x \)[/tex], divide both sides by 2:
[tex]\[ \frac{-12}{2} = \frac{2x}{2} \][/tex]
This simplifies to:
[tex]\[ x = -6 \][/tex]
So, the solution to the equation [tex]\( 2x - 2^2 = 4x + 8 \)[/tex] is:
[tex]\[ x = -6 \][/tex]
