Question

solve the inequality and express the solution set solution set on the real number line. -5(2x + 3) ≥ 34x - 3(x + 3)

Explanation:

Step1: Expand both sides

$-10x - 15 \geq 3[4x - 3x - 9]$
$-10x - 15 \geq 3(x - 9)$
$-10x - 15 \geq 3x - 27$

Step2: Isolate x terms

$-10x - 3x \geq -27 + 15$
$-13x \geq -12$

Step3: Solve for x (reverse inequality)

$x \leq \frac{12}{13}$

Step4: Graph on number line

Draw a closed dot at $\frac{12}{13}$, shade all values to the left.

Answer:

The solution set is $x \leq \frac{12}{13}$.

For the real number line: Place a filled (closed) circle at the point representing $\frac{12}{13}$, then draw a solid arrow extending to the left from this point to represent all real numbers less than or equal to $\frac{12}{13}$.