Question

I need some help please out

Answer 1

( - ∞, 1] U [3, ∞)

In other words,

`x\le1,x\ge3`

Explanation:

To solve the system given, we first get rid of the absolute value sign and decompose the inequality into two

`\begin{gathered} |4x-8|\ge4 \\ \rightarrow4x-8\ge4 \\ 4x-8\le-4 \end{gathered}`

Let is solve the two inequalities

`\begin{gathered} 4x-8\ge4 \\ \end{gathered}`

add 8 to both sides to get

`4x\ge12`

finally, divide both sides by 4 to get

`\boxed{x\ge3}`

Now for the second inequality

`4x-8\le-4`

adding 8 to both sides gives

`4x\le4`

Finally, dividing both sides by 4 gives

`\boxed{x\le1.}`

Hence, the solution to the system is

`x\le1,x\ge3`

which can be written as

`\mleft(-\infty,1\rbrack\cup\lbrack3,\infty\mright)`