Question

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

Answer 1

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 ^^

Answer 2

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!