Final answer:
To solve the inequality 52 - 3x < -14, you need to subtract 52 from both sides, which gives -3x < -66, and then divide by -3, which flips the inequality sign, resulting in x > 22.
Step-by-step explanation:
The inequality 52 - 3x < -14 can be solved step-by-step to find the range of values for x that make the inequality true. To do this, we first isolate the variable term on one side:
- Subtract 52 from both sides of the inequality: 52 - 3x - 52 < -14 - 52
- This simplifies to: -3x < -66.
- Next, divide both sides by -3, remembering that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign:
- The final solution is x > 22.
This means that for any value of x greater than 22, the original inequality will hold true.