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What is the solution to [tex]|x-6| \geq 5[/tex]?

A. [tex]1 \leq x \leq 11[/tex]

B. [tex]-11 \leq x \leq 1[/tex]

C. [tex]x \geq 11[/tex] or [tex]x \leq 1[/tex]

D. [tex]x \geq 1[/tex] or [tex]x \leq -11[/tex]

Sagot :

GinnyAnsweridn
Let's solve the inequality [tex]\(|x - 6| \geq 5\)[/tex].

The absolute value inequality [tex]\(|x - 6| \geq 5\)[/tex] can be split into two separate inequalities:
[tex]\[ x - 6 \geq 5 \][/tex]
and
[tex]\[ x - 6 \leq -5 \][/tex]

### Solving the First Inequality
[tex]\[ x - 6 \geq 5 \][/tex]
Add 6 to both sides:
[tex]\[ x \geq 11 \][/tex]

### Solving the Second Inequality
[tex]\[ x - 6 \leq -5 \][/tex]
Add 6 to both sides:
[tex]\[ x \leq 1 \][/tex]

### Combining the Results
From the inequalities, we have:
[tex]\[ x \geq 11 \][/tex]
or
[tex]\[ x \leq 1 \][/tex]

Therefore, the solution to the inequality [tex]\(|x - 6| \geq 5\)[/tex] is:
[tex]\[ x \geq 11 \text{ or } x \leq 1 \][/tex]

Hence, the correct answer is:

C. [tex]\( x \geq 11 \)[/tex] or [tex]\( x \leq 1 \)[/tex]
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