Question

which graph shows the solution set of the inequality 2.9(x + 8) < 26.1?

Explanation:

Step1: Expand the left - hand side

$2.9(x + 8)=2.9x+2.9\times8=2.9x + 23.2$
So the inequality becomes $2.9x+23.2<26.1$.

Step2: Isolate the variable term

Subtract 23.2 from both sides of the inequality:
$2.9x+23.2 - 23.2<26.1 - 23.2$
$2.9x<2.9$

Step3: Solve for x

Divide both sides of the inequality by 2.9:
$\frac{2.9x}{2.9}<\frac{2.9}{2.9}$
$x < 1$

The solution set on a number - line is an open circle at 1 (because x is less than 1, not less than or equal to 1) and an arrow pointing to the left.

Answer:

The graph with an open circle at 0 and an arrow pointing to the left (the fourth graph in the order presented in the image) represents the solution set of the inequality $2.9(x + 8)<26.1$.