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Popular >

4|z-5|-9>14

Solution

4 ∣ z - 5 ∣ - 9 > 14

Solution

z < - \frac{3}{4} or z > \frac{43}{4}

+2

Interval Notation

(- \infty, - \frac{3}{4}) \cup (\frac{43}{4}, \infty)

Decimal Notation

z < - 0.75 or z > 10.75

Solution steps

4 ∣ z - 5 ∣ - 9 > 14

Move

9

to the right side

4 ∣ z - 5 ∣ > 23

Divide both sides by

4

∣ z - 5 ∣ > \frac{23}{4}

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

or

u > a

z - 5 < - \frac{23}{4} or z - 5 > \frac{23}{4}

z - 5 < - \frac{23}{4} or z - 5 > \frac{23}{4}

z < - \frac{3}{4} or z > \frac{43}{4}

Popular Examples

x^{2} + 11 x + 30 = 0

factor x^3+3x^2+5x factor

x^{3} + 3 x^{2} + 5 x

simplify 4x^2+15x^3+4xy-2x^3 simplify

4 x^{2} + 15 x^{3} + 4 x y - 2 x^{3}

11 x + 4 < 15

|(x+3)/(2x)|<= 10

\frac{x + 3}{2 x} \leq 10

Frequently Asked Questions (FAQ)

What is 4|z-5|-9>14 ?
The solution to 4|z-5|-9>14 is z<-3/4 \lor z> 43/4