Question

Which value below is not included in the solution set for the inequality statement?

X + 4 ≥ 1/2 (x-3)
a. -13
b. -1
c. -3
d. 2

Answer 1

In the given inequality statement x + 4 ≥ 1/2 (x-3), x ≤ -8 is the solution set. The value that is not included in the solution set is -1 (option b).

Step-by-step explanation:

In the given inequality statement x + 4 ≥ 1/2 (x-3), we can find the solution set by solving the inequality.

Step 1: Distribute the 1/2 to the expression in the parentheses. x + 4 ≥ 1/2x - 3/2

Step 2: Combine like terms. x + 4 ≥ 1/2x - 3/2

Step 3: Subtract x from both sides to isolate the variable. 4 ≥ -1/2x - 3/2

Step 4: Simplify the inequality. 4 + 3/2 ≥ -1/2x

Step 5: Multiply both sides by -2 to solve for x. -8 ≥ x

Therefore, the solution set for the inequality is x ≤ -8.

Out of the given options, the value that is not included in the solution set is -1 (option b).