Question

other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line.
3(x - 1) - 5(x + 1) ≥ -2x - 5
select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. the solution set is (type your answer in interval notation.)
b. the solution set is ∅

Explanation:

Step1: Expand the left side

First, we expand \(3(x - 1)-5(x + 1)\). Using the distributive property \(a(b + c)=ab+ac\), we get:
\(3x-3-5x - 5\)
Combine like terms: \((3x-5x)+(-3 - 5)=-2x-8\)
So the inequality becomes \(-2x-8\geq - 2x-5\)

Step2: Add \(2x\) to both sides

Add \(2x\) to both sides of the inequality \(-2x-8\geq - 2x-5\):
\(-2x + 2x-8\geq - 2x+2x - 5\)
Simplify: \(-8\geq - 5\)

Answer:

B. The solution set is \(\varnothing\)