Question

solve the compound linear inequality graphically. write the solution set in interval notation, and approximate endpoints to the nearest tenth whenever appropriate.$1.3 \leq 9.1 - 0.6x \leq 6.4$choose the correct graph on the right.

Explanation:

Step1: Subtract 9.1 from all parts

$1.3 - 9.1 \leq 9.1 - 0.6x - 9.1 \leq 6.4 - 9.1$
$\implies -7.8 \leq -0.6x \leq -2.7$

Step2: Divide by -0.6 (reverse inequalities)

$\frac{-7.8}{-0.6} \geq x \geq \frac{-2.7}{-0.6}$
$\implies 13 \geq x \geq 4.5$
$\implies 4.5 \leq x \leq 13$

Step3: Match to correct graph

The interval $[4.5, 13]$ corresponds to a number line with closed dots at 4.5 and 13, shaded between them. This matches graph A.

Answer:

Solution set in interval notation: $[4.5, 13]$
Correct graph: A. (The graph with closed endpoints at 4.5 and 13, shaded between the two points)