Question

solve the inequality. graph the solution. |4x - 2|+5>11. choose the correct graph below. a. graph description with points and number - line, b. graph description with points and number - line, c. graph description with points and number - line, d. graph description with points and number - line, e. graph description with points and number - line, f. graph description with points and number - line. help me solve this view an example get more help - review progress question 16 of 20

Explanation:

Step1: Isolate absolute - value

$|4x - 2|+5>11$ becomes $|4x - 2|>6$.

Step2: Split into two inequalities

$4x - 2>6$ or $4x - 2<-6$.

Step3: Solve first inequality

$4x - 2>6$, so $4x>8$ and $x > 2$.

Step4: Solve second inequality

$4x - 2<-6$, so $4x<-4$ and $x<-1$.

Answer:

The solution is $x < - 1$ or $x>2$. The graph would be an open - circle at $x=-1$ with a line extending to the left and an open - circle at $x = 2$ with a line extending to the right (similar to option F).