It seems there are some errors in the steps provided. Let's solve the equation [tex]\( 2x - 3 = 30 - (x - 12) \)[/tex] step-by-step correctly.
Step-by-Step Solution:
1. Distribute the negative sign inside the parentheses on the right side of the equation:
[tex]\[
2x - 3 = 30 - x + 12
\][/tex]
2. Combine like terms on the right side:
[tex]\[
2x - 3 = 42 - x
\][/tex]
3. Move the [tex]\( -x \)[/tex] term to the left side by adding [tex]\( x \)[/tex] to both sides:
[tex]\[
2x + x - 3 = 42
\][/tex]
Which simplifies to:
[tex]\[
3x - 3 = 42
\][/tex]
4. Move the [tex]\( -3 \)[/tex] term to the right side by adding 3 to both sides:
[tex]\[
3x = 42 + 3
\][/tex]
Which simplifies to:
[tex]\[
3x = 45
\][/tex]
5. Solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[
x = \frac{45}{3}
\][/tex]
[tex]\[
x = 15
\][/tex]
Therefore, the correct solution to the equation [tex]\( 2x - 3 = 30 - (x - 12) \)[/tex] is [tex]\( x = 15 \)[/tex].
