Question

Solve each inequality and grap 4(3x+3)<=48

Answer 1

The inequality 4(3x+3) ≤ 48 is solved by distributing, subtracting 12, and dividing by 12, resulting in x ≤ 3. The graph would show a closed circle at 3 with shading to the left.

Step-by-step explanation:

To solve the inequality 4(3x+3) ≤ 48, we need to follow these steps:

1. Distribute the 4 into the parentheses: 4 × 3x + 4 × 3 ≤ 48, which simplifies to 12x + 12 ≤ 48.
2. Subtract 12 from both sides to isolate the term with x: 12x + 12 - 12 ≤ 48 - 12, which simplifies to 12x ≤ 36.
3. Divide both sides by 12 to solve for x: 12x / 12 ≤ 36 / 12, resulting in x ≤ 3.

To graph this inequality, you would draw a number line, make a closed circle at 3 (since it is ≤, not just <) and shade to the left, indicating all x values that are less than or equal to 3 are solutions to the inequality.