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Popular >

|4x-3|+2<10

Solution

∣ 4 x - 3 ∣ + 2 < 10

Solution

- \frac{5}{4} < x < \frac{11}{4}

+2

Interval Notation

(- \frac{5}{4}, \frac{11}{4})

Decimal Notation

- 1.25 < x < 2.75

Solution steps

∣ 4 x - 3 ∣ + 2 < 10

Move

2

to the right side

∣ 4 x - 3 ∣ < 8

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 8 < 4 x - 3 < 8

4 x - 3 > - 8 and 4 x - 3 < 8

x > - \frac{5}{4} and x < \frac{11}{4}

Merge Overlapping Intervals

- \frac{5}{4} < x < \frac{11}{4}

Popular Examples

\frac{2}{∣ x - 4 ∣} > 1

log_{2}(|x-2|)>log_{2}(|x+4|)

lo g_{2} (∣ x - 2 ∣) > lo g_{2} (∣ x + 4 ∣)

|x+1|^2+2|x+2|>= 2

∣ x + 1 ∣^{2} + 2 ∣ x + 2 ∣ \geq 2

|x^2-2x|+|x-4|<|x^2-3x+4|

x^{2} - 2 x + ∣ x - 4 ∣ < x^{2} - 3 x + 4

∣ - 6 (n + 5) ∣ > - 12

Frequently Asked Questions (FAQ)

What is |4x-3|+2<10 ?
The solution to |4x-3|+2<10 is -5/4 <x< 11/4