Question

Question is shown in image below. Answer format is also shown in image.

Answer 1

For |2x-7|>1:

This absolute value inequality results in two inequalities: 2x-7>1 or 2x-7<-1.

Solve these inequalities to find the answer:

$\begin{gathered} 2x-7>1 \\ 2x>1+7 \\ x>\frac{8}{2} \\ x>4 \end{gathered}$$\begin{gathered} 2x-7<-1 \\ 2x<-1+7 \\ x<\frac{6}{2} \\ x<3 \end{gathered}$

It means that the answer is x>4; x<3.

For |2x-7|<1:

This results in one complex inequality: -1<2x-7<1.

Solve it to find the answer:

$\begin{gathered} -1<2x-7<1 \\ -1+7<2x<1+7 \\ 6<2x<8 \\ \frac{6}{2}It means that the answer is 3For |2x-7|=1:From the equation we can conclude that 2x-7=1 or 2x-7=-1.Solve these equations to find the answer:[tex]\begin{gathered} 2x-7=1 \\ 2x=1+7 \\ x=\frac{8}{2} \\ x=4 \end{gathered}$$\begin{gathered} 2x-7=-1 \\ 2x=-1+7 \\ x=\frac{6}{2} \\ x=3 \end{gathered}$The answer is x=3; x=4.