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Sagot :
Answer:
( - ∞, 1] U [3, ∞)
In other words,
[tex]x\le1,x\ge3[/tex]Explanation:
To solve the system given, we first get rid of the absolute value sign and decompose the inequality into two
[tex]\begin{gathered} |4x-8|\ge4 \\ \rightarrow4x-8\ge4 \\ 4x-8\le-4 \end{gathered}[/tex]Let is solve the two inequalities
[tex]\begin{gathered} 4x-8\ge4 \\ \end{gathered}[/tex]add 8 to both sides to get
[tex]4x\ge12[/tex]finally, divide both sides by 4 to get
[tex]\boxed{x\ge3}[/tex]Now for the second inequality
[tex]4x-8\le-4[/tex]adding 8 to both sides gives
[tex]4x\le4[/tex]Finally, dividing both sides by 4 gives
[tex]\boxed{x\le1.}[/tex]Hence, the solution to the system is
[tex]x\le1,x\ge3[/tex]which can be written as
[tex]\mleft(-\infty,1\rbrack\cup\lbrack3,\infty\mright)[/tex]
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