Let's solve the equation step-by-step to determine the correct value of \( x \).
Given equation:
[tex]\[ 2x - 3x - 18 = -18 + 2x + 5x \][/tex]
First, simplify both sides of the equation:
On the left side:
[tex]\[ 2x - 3x - 18 \][/tex]
[tex]\[ = -x - 18 \][/tex]
On the right side:
[tex]\[ -18 + 2x + 5x \][/tex]
[tex]\[ = -18 + 7x \][/tex]
So the simplified equation becomes:
[tex]\[ -x - 18 = -18 + 7x \][/tex]
Next, we will isolate the variable \( x \):
Add \( 18 \) to both sides of the equation:
[tex]\[ -x - 18 + 18 = -18 + 7x + 18 \][/tex]
This simplifies to:
[tex]\[ -x = 7x \][/tex]
Now, add \( x \) to both sides to combine the \( x \) terms:
[tex]\[ -x + x = 7x + x \][/tex]
This simplifies to:
[tex]\[ 0 = 8x \][/tex]
Now, solve for \( x \) by dividing both sides by 8:
[tex]\[ \frac{0}{8} = x \][/tex]
[tex]\[ 0 = x \][/tex]
[tex]\[ x = 0 \][/tex]
We have isolated \( x \) and found that \( x = 0 \).
Therefore, the correct answer is:
[tex]\[ x = 0 \][/tex]
