What is the solution to [tex]-3(x-6)\ \textgreater \ 2x-2[/tex]?

A. [tex]x\ \textgreater \ 4[/tex]
B. [tex]x\ \textgreater \ -16[/tex]
C. [tex]x\ \textless \ 4[/tex]
D. [tex]x\ \textless \ -16[/tex]



Answer :

To solve the inequality [tex]\(-3(x-6) > 2x - 2\)[/tex], we will go through it step by step.

1. Distribute the [tex]\(-3\)[/tex] on the left side:
[tex]\[ -3(x - 6) = -3 \cdot x + -3 \cdot (-6) = -3x + 18 \][/tex]
So the inequality becomes:
[tex]\[ -3x + 18 > 2x - 2 \][/tex]

2. Move all terms involving [tex]\(x\)[/tex] to one side and constants to the other:
Add [tex]\(3x\)[/tex] to both sides:
[tex]\[ 18 > 5x - 2 + 3x \][/tex]
Simplify:
[tex]\[ 18 > 5x - 2 \][/tex]

3. Add 2 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ 18 + 2 > 5x \][/tex]
Simplify:
[tex]\[ 20 > 5x \][/tex]

4. Divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{20}{5} > x \][/tex]
Simplify:
[tex]\[ 4 > x \][/tex]

Or equivalently,
[tex]\[ x < 4 \][/tex]

Thus, the solution to [tex]\(-3(x-6) > 2 x - 2\)[/tex] is:
[tex]\[ x < 4 \][/tex]

Therefore, the correct answer is:
[tex]\[ (2) \, x < 4 \][/tex]