Question

Which list contains only values that are solutions to the inequality

-4x-19>33

1)-15,-14-13
2)-12-11-10
3)-13-12-11-10
4)-15-14

Answer 1

To find the solutions to the inequality \(-4x - 19 > 33\), we will first solve for \(x\).

1. Start by isolating the term with \(x\) on one side:
\[
-4x - 19 > 33
\]

2. Add 19 to both sides:
\[
-4x > 33 + 19
\]
\[
-4x > 52
\]

3. Divide both sides by -4. Remember that when you divide or multiply by a negative number, you must flip the inequality sign:
\[
x < \frac{52}{-4}
\]
\[
x < -13
\]

Now that we know the solution to the inequality is \(x < -13\), we can check the lists provided to see which one contains only values that are less than -13.

1. **List 1:** -15, -14, -13
- -15 < -13 (satisfies)
- -14 < -13 (satisfies)
- -13 is not less than -13 (does not satisfy)

Not a valid choice.

2. **List 2:** -12, -11, -10
- -12 is not less than -13 (does not satisfy)
- -11 is not less than -13 (does not satisfy)
- -10 is not less than -13 (does not satisfy)

Not a valid choice.

3. **List 3:** -13, -12, -11, -10
- -13 is not less than -13 (does not satisfy)
- -12 is not less than -13 (does not satisfy)
- -11 is not less than -13 (does not satisfy)
- -10 is not less than -13 (does not satisfy)

Not a valid choice.

4. **List 4:** -15, -14
- -15 < -13 (satisfies)
- -14 < -13 (satisfies)

This is a valid choice.

The correct answer is **List 4: -15, -14**.