Question

Which given value(s) make the inequality true?

5h + 12 < -3
h = -3; h = -4; h = -5
O h = -5
Oh=-3
Oh=-4
0 h = -3; h = -4; h = -5

Answer 1

To solve 5h + 12 < -3h, we isolate h to find that h < -1.5. Upon checking the given values, all of them (h = -3, h = -4, and h = -5) satisfy the inequality because they are less than -1.5.

Step-by-step explanation:

The question asks which given value(s) make the inequality 5h + 12 < -3h true. Let's solve the inequality step-by-step:

1. Add 3h to both sides of the inequality: 5h + 3h + 12 < 0.
2. Simplify the inequality: 8h + 12 < 0.
3. Subtract 12 from both sides: 8h < -12.
4. Divide both sides by 8: h < -12/8.
5. Simplify the division: h < -1.5.

All values of h that are less than -1.5 will make the inequality true.

Now, let's evaluate the given values:

• For h = -3, we have 5(-3) + 12 = -15 + 12 = -3. Since -3 is less than 0, h = -3 satisfies the inequality.
• For h = -4, we have 5(-4) + 12 = -20 + 12 = -8. Since -8 is less than 0, h = -4 also satisfies the inequality.
• For h = -5, we have 5(-5) + 12 = -25 + 12 = -13. Since -13 is less than 0, h = -5 also satisfies the inequality.

Therefore, the values that make the inequality true are h = -3, h = -4, and h = -5.