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Popular >

|x-2|+2<3

Solution

∣ x - 2 ∣ + 2 < 3

Solution

1 < x < 3

+1

Interval Notation

(1, 3)

Solution steps

∣ x - 2 ∣ + 2 < 3

Move

2

to the right side

∣ x - 2 ∣ < 1

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 1 < x - 2 < 1

x - 2 > - 1 and x - 2 < 1

x > 1 and x < 3

Merge Overlapping Intervals

1 < x < 3

Popular Examples

simplify (x^{2n+1})/(x^{2n-1)}simplify

\frac{x ^{2 n + 1}}{x ^{2 n - 1}}

factor 6x-30 factor

6 x - 30

-4a+13>= 29\land 10<6a-14

- 4 a + 13 \geq 29 and 10 < 6 a - 14

-1/6 (x-18)+1/3 (x+3)=x+4

- \frac{1}{6} (x - 18) + \frac{1}{3} (x + 3) = x + 4

factor 49x^2+126x+81 factor

49 x^{2} + 126 x + 81

Frequently Asked Questions (FAQ)

What is |x-2|+2<3 ?
The solution to |x-2|+2<3 is 1<x<3