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Popular >

|z+9|+1>= 4

Solution

∣ z + 9 ∣ + 1 \geq 4

Solution

z \leq - 12 or z \geq - 6

+1

Interval Notation

(- \infty, - 12] \cup [- 6, \infty)

Solution steps

∣ z + 9 ∣ + 1 \geq 4

Move

1

to the right side

∣ z + 9 ∣ \geq 3

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

z + 9 \leq - 3 or z + 9 \geq 3

z + 9 \leq - 3 or z + 9 \geq 3

z \leq - 12 or z \geq - 6

Popular Examples

x^{2} - 9 x + 2 = 0

factor ((6a^2b+12ab^2+6b^2))/((a^2-b^2))factor

\frac{( 6 a ^{2} b + 12 a b ^{2} + 6 b ^{2} )}{( a ^{2} - b ^{2} )}

factor (a-4)^2-2(a-4)factor

(a - 4)^{2} - 2 (a - 4)

12x^2-220x+600=0

12 x^{2} - 220 x + 600 = 0

simplify (4a^2+3a+2)/(a^3-1)-(1-2a)/(a^2+a+1)simplify

\frac{4 a ^{2} + 3 a + 2}{a ^{3} - 1} - \frac{1 - 2 a}{a ^{2} + a + 1}

Frequently Asked Questions (FAQ)

What is |z+9|+1>= 4 ?
The solution to |z+9|+1>= 4 is z<=-12\lor z>=-6