Question

graph your solution to the inequality. $\frac{2}{7}|4f + 6|-2geq10$

Explanation:

Step1: Isolate the absolute - value expression

Add 2 to both sides of the inequality $\frac{2}{7}|4f + 6|-2\geq10$.
$\frac{2}{7}|4f + 6|\geq10 + 2$, so $\frac{2}{7}|4f + 6|\geq12$.
Then multiply both sides by $\frac{7}{2}$: $|4f+6|\geq12\times\frac{7}{2}$, and $|4f + 6|\geq42$.

Step2: Split the absolute - value inequality

We get two inequalities:

1. $4f+6\geq42$. Subtract 6 from both sides: $4f\geq42 - 6$, so $4f\geq36$. Divide both sides by 4: $f\geq9$.
2. $4f + 6\leq-42$. Subtract 6 from both sides: $4f\leq-42 - 6$, so $4f\leq-48$. Divide both sides by 4: $f\leq-12$.

Answer:

The solution of the inequality is $f\leq-12$ or $f\geq9$. On the number - line, we mark a closed circle at $f=-12$ and shade to the left, and mark a closed circle at $f = 9$ and shade to the right.