Question

which graph shows the solution set of the inequality 2.9(x + 8) < 28.1?

Explanation:

Step1: Expand the left - hand side

$2.9(x + 8)=2.9x+2.9\times8=2.9x + 23.2$
So the inequality becomes $2.9x+23.2<28.1$.

Step2: Isolate the variable term

Subtract 23.2 from both sides:
$2.9x+23.2 - 23.2<28.1 - 23.2$
$2.9x<4.9$

Step3: Solve for x

Divide both sides by 2.9:
$x<\frac{4.9}{2.9}\approx1.69$

The solution set is all real numbers less than approximately 1.69. On a number - line, this is represented by an open circle at the value (since the inequality is strict, $x
eq1.69$) and an arrow pointing to the left.

Answer:

The graph with an open circle at a value slightly greater than 0 and an arrow pointing to the left. (Based on the fact that $x < \frac{4.9}{2.9}\approx1.69$, the open - circle should be to the right of 0 and the arrow should point left).