Let's solve the equation step-by-step:
Given equation:
[tex]\[ 4x - 3 + 5 = 2x + 7 - 8x \][/tex]
1. Simplify both sides of the equation by combining like terms:
On the left side:
[tex]\[ 4x - 3 + 5 \][/tex]
Combine [tex]\(-3\)[/tex] and [tex]\(5\)[/tex]:
[tex]\[ 4x + 2 \][/tex]
On the right side:
[tex]\[ 2x + 7 - 8x \][/tex]
Combine [tex]\(2x\)[/tex] and [tex]\(-8x\)[/tex]:
[tex]\[ -6x + 7 \][/tex]
Now the equation is:
[tex]\[ 4x + 2 = -6x + 7 \][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side of the equation and constant terms to the other side:
Add [tex]\(6x\)[/tex] to both sides:
[tex]\[ 4x + 6x + 2 = 7 \][/tex]
[tex]\[ 10x + 2 = 7 \][/tex]
Subtract [tex]\(2\)[/tex] from both sides:
[tex]\[ 10x = 5 \][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(10\)[/tex]:
[tex]\[ x = \frac{5}{10} \][/tex]
[tex]\[ x = \frac{1}{2} \][/tex]
So the correct answer is:
C. [tex]\(x = \frac{1}{2}\)[/tex]
