Question

Can someone help me with these interval notations?
|4-3x| <= 13

Answer 1

To solve the inequality |4-3x| ≤ 13, consider two cases: when 4-3x ≤ 13 and when -(4-3x) ≤ 13. Solve each case separately, then combine the solutions. The solution to the inequality is x ≥ 5.67.

Step-by-step explanation:

To solve the inequality |4-3x| ≤ 13, we need to consider two cases:

1. When 4-3x ≤ 13:

• Subtract 4 from both sides: -3x ≤ 9.
• Divide both sides by -3. Since we are dividing by a negative number, we must reverse the inequality sign: x ≥ -3.

When -(4-3x) ≤ 13:

• Expand the absolute value by multiplying -1 inside: -4+3x ≤ 13.
• Add 4 to both sides: 3x ≥ 17.
• Divide both sides by 3: x ≥ 5.67 (approximately).

Combining the two cases, we find that x ≥ -3 and x ≥ 5.67. Therefore, the solution is x ≥ 5.67.