Question

solve the following inequality.
0.5x + 5 ≤ 1.3x - 4

select the correct choice below and fill in the answer box to complete your choice.

a. the solution set is {x|x ≤}

b. the solution set is {x|x ≥}

c. the solution set is {x|x >}

d. the solution set is {x|x <}

Explanation:

Step1: Move x - terms to one side

Subtract \(0.5x\) from both sides:
\(0.5x + 5-0.5x\leq1.3x - 4-0.5x\)
\(5\leq0.8x - 4\)

Step2: Move constant - terms to one side

Add 4 to both sides:
\(5 + 4\leq0.8x-4 + 4\)
\(9\leq0.8x\)

Step3: Solve for x

Divide both sides by 0.8:
\(x\geq\frac{9}{0.8}=\frac{90}{8}=\frac{45}{4}=11.25\)

Answer:

B. The solution set is \(\{x|x\geq11.25\}\)