Question

Which values are solutions to the below check all that apply x² ≤64:

-10, -5, 0, 5, 10

Option A: -10, -5, 0, 5, 10
Option B: -10, 0, 10
Option C: -5, 0, 5
Option D: 5, 10

Answer 1

To determine which values are solutions to the inequality x² ≤ 64, we need to solve the inequality by taking the square root of both sides. The values of x that satisfy this condition are between -10 and 8. All other given options do not fulfill the inequality.

Step-by-step explanation:

To determine which values are solutions to the inequality x² ≤ 64, we need to find the values of x that satisfy this condition. One way to solve this is by taking the square root of both sides of the inequality. Since the square root of a number always gives us a positive value, we have two cases to consider:

Case 1: x is positive or zero

√(x²) ≤ √64

x ≤ 8

Therefore, all values of x between -10 and 8 (inclusive) satisfy the inequality.

Case 2: x is negative

Since the square of a negative number is positive, any negative value for x will not satisfy the inequality.

Hence, the correct option is A: -10, -5, 0, 5, 10.