absolutle value inequalities?

[kmecx0love]

Question: Solve the following inequality. Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter ∞ as infinity and −∞ as -infinity .

|x + 1| ≥ 2



so..i basically have no idea where to start. i know that you have to subtract the 2 and make the > sign an = sign..
but that leaves me at |x+1| -2 = 0 and idk where to go from there..

[Subhotosh Khan]

Question: Solve the following inequality. Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter ∞ as infinity and −∞ as -infinity .

|x + 1| ≥ 2



so..i basically have no idea where to start. i know that you have to subtract the 2 and make the > sign an = sign..
but that leaves me at |x+1| -2 = 0 and idk where to go from there..

(x+1) - 2 ≥ 0 .......................................... -(x-1) - 2 ≥ 0

x - 1 ≥ 0 ............................................... - x - 1 ≥ 0

Now continue.....

[Mrspi]

Question: Solve the following inequality. Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter ∞ as infinity and −∞ as -infinity .

|x + 1| ≥ 2



so..i basically have no idea where to start. i know that you have to subtract the 2 and make the > sign an = sign..
but that leaves me at |x+1| -2 = 0 and idk where to go from there..

"absolute value" is the same thing as "distance from 0 on the number line."

If the absolute value of "something" is > 2, then that "something" must be 2 or more units from 0 on the number line.

So,

that "something" > 2, or that "something" < -2

The "something" in your problem is x + 1.... so,

x + 1 > 2 OR x + 1 < -2

Solve each of those inequalities. The solution for the original problem is the UNION of the two solution sets for the inequalities.