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Popular >

|2x+3|+1<11

Solution

∣ 2 x + 3 ∣ + 1 < 11

Solution

- \frac{13}{2} < x < \frac{7}{2}

+2

Interval Notation

(- \frac{13}{2}, \frac{7}{2})

Decimal Notation

- 6.5 < x < 3.5

Solution steps

∣ 2 x + 3 ∣ + 1 < 11

Move

1

to the right side

∣ 2 x + 3 ∣ < 10

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 10 < 2 x + 3 < 10

2 x + 3 > - 10 and 2 x + 3 < 10

x > - \frac{13}{2} and x < \frac{7}{2}

Merge Overlapping Intervals

- \frac{13}{2} < x < \frac{7}{2}

Popular Examples

∣ u ∣ + 5 < 12

∣ 7 - 2 x ∣ = 15

(-3x)/(x^2-9)>0

\frac{- 3 x}{x ^{2} - 9} > 0

(x-8)/(x+2)>= 0

\frac{x - 8}{x + 2} \geq 0

simplify (sqrt(4))/(2sqrt(20))simplify

\frac{4}{2 20}

Frequently Asked Questions (FAQ)

What is |2x+3|+1<11 ?
The solution to |2x+3|+1<11 is -13/2 <x< 7/2