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Rainbow [258]
3 years ago
8

Solve the following inequality algebraically. ∣x−9∣≥4

Mathematics
2 answers:
Naya [18.7K]3 years ago
3 0

Answer:

x ≥ 13 or x ≤ 5

Step-by-step explanation:

First, apply absolute value rule:

x - 9 ≥ 4 or x - 9 ≤ -4

Then, add 9 on both sides with both inequalities:

x ≥ 13 or x ≤ 5

This is a disjunction, so you can't combine the inequalities.

Hope this helps ^^

myrzilka [38]3 years ago
3 0

Answer:

x\geq 13\text{ or }x\leq  5

Step-by-step explanation:

So we have the inequality:

|x-9|\geq 4

Definition of Absolute Value. Since this is "greater than," we need to use "or."

x-9\geq 4\text{ or }x-9\leq -4

Also, note that we flip the inequality on the second equation because we multiplied by a negative.

Add 9 to both equations:

x\geq 13\text{ or }x\leq  5

And that's our solution.

And we're done!

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