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Popular >

|2x+5|+2<8

Solution

∣ 2 x + 5 ∣ + 2 < 8

Solution

- \frac{11}{2} < x < \frac{1}{2}

+2

Interval Notation

(- \frac{11}{2}, \frac{1}{2})

Decimal Notation

- 5.5 < x < 0.5

Solution steps

∣ 2 x + 5 ∣ + 2 < 8

Move

2

to the right side

∣ 2 x + 5 ∣ < 6

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 6 < 2 x + 5 < 6

2 x + 5 > - 6 and 2 x + 5 < 6

x > - \frac{11}{2} and x < \frac{1}{2}

Merge Overlapping Intervals

- \frac{11}{2} < x < \frac{1}{2}

Popular Examples

3/5 n+9/10 =-1/5 n-23/10

\frac{3}{5} n + \frac{9}{10} = - \frac{1}{5} n - \frac{23}{10}

factor 13n^2+10n-3 factor

13 n^{2} + 10 n - 3

2^{4} \cdot 3^{2}

\frac{y}{5} + \frac{y}{2} = 7

20 - \frac{x}{3} = \frac{x}{2}

Frequently Asked Questions (FAQ)

What is |2x+5|+2<8 ?
The solution to |2x+5|+2<8 is -11/2 <x< 1/2