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Solve the inequality algebraically. Express your answer using set notation or interval notation. l x-8l greater than or equal to 4. Rewrite the inequality without the absolute values.

Solve The Inequality Algebraically Express Your Answer Using Set Notation Or Interval Notation L X8l Greater Than Or Equal To 4 Rewrite The Inequality Without T class=

Sagot :

To rewrite the inequality:

[tex]\lvert{x-8}\rvert\ge4[/tex]

we need to remember that:

[tex]\lvert{x}\rvert\ge a\text{ is equivalent to }x\ge a\text{ or }x\leq-a[/tex]

Then in this case we have:

[tex]\begin{gathered} \lvert{x-8}\rvert\ge4 \\ \text{ Is equivalent to:} \\ x-8\ge4\text{ or }x-8\leq-4 \end{gathered}[/tex]

Therefore, we can rewrite the inequality as:

[tex]x-8\leq-4\text{ or }x-8\ge4[/tex]

Once we have it written in this form we can solve it:

[tex]\begin{gathered} x-8\leq-4\text{ or }x-8\ge4 \\ x\leq-4+8\text{ or }x\ge4+8 \\ x\leq4\text{ or }x\ge12 \end{gathered}[/tex]

Therefore, the solution set of the inequality is:

[tex](-\infty,4\rbrack\cup\lbrack12,\infty)[/tex]

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