Question

Mary is using the set

{4, 5, 6, 7, 8} to solve the
inequality shown.

7-8x>-41

Select all the solutions to
the inequality.

Answer 1

To solve the inequality 7-8x>-41, first simplify to get x<6. Then, numbers 4 and 5 from the set {4, 5, 6, 7, 8} are identified as solutions because they are less than 6.

Step-by-step explanation:

The student is asking how to find the solutions to the inequality 7 - 8x > -41 using the given set {4, 5, 6, 7, 8}. To do this, one must solve the inequality for x and then test the values from the set to determine which are solutions.

First, we need to isolate x:

1. Add 8x to both sides of the inequality: 7 > 8x - 41
2. Add 41 to both sides of the inequality: 7 + 41 > 8x
3. Divide both sides by 8: (48/8) > x or x < 6

Next, we test the numbers from the set:

• 4: Lagitimate solution since 4 is less than 6
• 5: Legitimate solution since 5 is less than 6

But 6, 7, and 8 are not solutions because they are not less than 6. Therefore, the solutions to the inequality from the given set are 4 and 5.