Solve the inequality 3(x-2) < 2x - 12 for x.
Check the final answer first, then review the worked steps.
Problem
Solve the inequality $3(x-2) < 2x - 12$ for x.
Answer
\(x < -6\)
Step-by-step solution
1. Distribute on the left side: Apply the distributive property to the left side of the inequality by multiplying 3 by each term inside the parentheses.
$$3(x - 2) < 2x - 12$$
$$3x - 6 < 2x - 12$$
2. Isolate the x terms: Subtract $2x$ from both sides of the inequality to move all terms containing $x$ to one side.
$$3x - 6 - 2x < 2x - 12 - 2x$$
$$x - 6 < -12$$
3. Isolate the constant terms: Add 6 to both sides of the inequality to move all constant terms to the other side, leaving $x$ by itself.
$$x - 6 + 6 < -12 + 6$$
$$x < -6$$