Question

which of the following shows the solution for the inequality 3.9(x + 3.8) ≥ 21.3 + 3x? a. number - line with closed - circle at 5 b. number - line with open - circle at 5 c. number - line with closed - circle at 7 d. number - line with open - circle at 7

Explanation:

Step1: Expand the left - hand side

$3.9(x + 3.8)=3.9x+3.9\times3.8 = 3.9x + 14.82$

Step2: Rewrite the inequality

$3.9x + 14.82\geq21.3+3x$

Step3: Subtract $3x$ from both sides

$3.9x-3x + 14.82\geq21.3+3x-3x$
$0.9x+14.82\geq21.3$

Step4: Subtract 14.82 from both sides

$0.9x+14.82 - 14.82\geq21.3-14.82$
$0.9x\geq6.48$

Step5: Divide both sides by 0.9

$\frac{0.9x}{0.9}\geq\frac{6.48}{0.9}$
$x\geq7.2$

A closed - circle is used for $\geq$ or $\leq$ and an open - circle is used for $>$ or $<$. The solution $x\geq7.2$ is represented by a closed - circle at 7.2 and an arrow pointing to the right.

Answer:

C.