Question

For which values of x is the inequality 2x + 19 > 3.3 – 19 true?

a) x < -15.7
b) x > 15.7
c) -15.7 < x < 15.7
d) x = -15.7

Answer 1

The inequality 2x + 19 > 3.3 - 19 simplifies to x > -17.35. This means the inequality is true for all x values greater than -17.35. The closest matching option is b) x > 15.7, but this may indicate an error, as it does not match the calculated value.

Step-by-step explanation:

To find the values of x for which the inequality 2x + 19 > 3.3 – 19 is true, let's simplify the inequality step by step:

1. Add 19 to both sides: 2x + 19 + 19 > 3.3.
2. Simplify the left side: 2x + 38 > 3.3.
3. Subtract 38 from both sides to isolate the term with x: 2x > -34.7.
4. Divide both sides by 2 to solve for x: x > -17.35.

This means that the inequality is true for all x values greater than -17.35. Among the options given, the closest option is b) x > 15.7. However, since the calculated threshold is -17.35, the provided options may not accurately reflect the correct interval. It's possible that there is a typo in the question or the options, and we should seek clarification.