Question

which of the following number lines represents the solution set of the inequality 4x - 3 ≥ -5x + 15?

Explanation:

Step1: Isolate variable terms

Add $5x$ to both sides: $4x + 5x-3\geq - 5x+5x + 15$, which simplifies to $9x-3\geq15$.

Step2: Isolate the variable further

Add 3 to both sides: $9x-3 + 3\geq15 + 3$, resulting in $9x\geq18$.

Step3: Solve for x

Divide both sides by 9: $\frac{9x}{9}\geq\frac{18}{9}$, so $x\geq2$.
On a number - line, $x\geq2$ is represented by a closed circle at 2 (because the inequality includes equality) and an arrow pointing to the right.

Answer:

The third number - line (the one with a closed circle at 2 and an arrow pointing to the right)