Solve ∣2𝑥−3∣≤7∣2x−3∣≤7.

To solve the inequality |2x - 3| ≤ 7, we need to consider two cases because of the absolute value.

Case 1: 2x - 3 ≤ 7 To solve this, we add 3 to both sides to isolate the term with x: 2x ≤ 7 + 3 2x ≤ 10 Then, we divide both sides by 2 to solve for x: x ≤ 5

Case 2: -(2x - 3) ≤ 7 To solve this, we distribute the negative sign: -2x + 3 ≤ 7 Then, we subtract 3 from both sides: -2x ≤ 7 - 3 -2x ≤ 4 Next, we divide both sides by -2, remembering to flip the inequality sign because we're dividing by a negative number: x ≥ -2

So, the solution to the inequality |2x - 3| ≤ 7 is -2 ≤ x ≤ 5.