Question

Solve the following inequality and graph it on a number line:

3(x – 4) < x – 6
What is the solution to this inequality?

A) x < 3
B) x > 3
C) x < 6
D) x > 6

Answer 1

To solve the inequality 3(x - 4) < x - 6, distribute the 3 and isolate x to find x < 3. Graph the solution on a number line as a shaded interval to the left of 3.

Step-by-step explanation:

To solve the inequality 3(x - 4) < x - 6, we start by distributing the 3: 3x - 12 < x - 6. Next, we can subtract x from both sides of the inequality to get 2x - 12 < -6. Then, we add 12 to both sides: 2x < 6. Finally, we divide both sides by 2 to isolate x: x < 3. So, the solution to the inequality is x < 3.

To graph the solution on a number line, we represent the solution as a shaded interval to the left of 3. The graph would look like this: