Let's solve the given equation step by step:
The equation is:
[tex]\[ 2x - 3x - 18 = -18 + 2x + 5x \][/tex]
1. Combine like terms on both sides of the equation:
On the left side:
[tex]\[ 2x - 3x = -x \][/tex]
So the equation becomes:
[tex]\[ -x - 18 = -18 + 2x + 5x \][/tex]
On the right side:
[tex]\[ 2x + 5x = 7x \][/tex]
So now the equation is:
[tex]\[ -x - 18 = -18 + 7x \][/tex]
2. Add 18 to both sides to simplify:
[tex]\[ -x - 18 + 18 = -18 + 7x + 18 \][/tex]
Simplifying both sides:
[tex]\[ -x = 7x \][/tex]
3. Move all x terms to one side of the equation:
Subtract [tex]\(7x\)[/tex] from both sides:
[tex]\[ -x - 7x = 0 \][/tex]
Simplify:
[tex]\[ -8x = 0 \][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by -8:
[tex]\[ x = \frac{0}{-8} \][/tex]
Simplify:
[tex]\[ x = 0 \][/tex]
So, the solution for [tex]\(x\)[/tex] is:
[tex]\[ x = 0 \][/tex]
The correct answer is [tex]\( x = 0 \)[/tex].
