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Popular >

9|1+8n|-3>= 78

Solution

9 ∣ 1 + 8 n ∣ - 3 \geq 78

Solution

n \leq - \frac{5}{4} or n \geq 1

+2

Interval Notation

(- \infty, - \frac{5}{4}] \cup [1, \infty)

Decimal Notation

n \leq - 1.25 or n \geq 1

Solution steps

9 ∣ 1 + 8 n ∣ - 3 \geq 78

Move

3

to the right side

9 ∣ 1 + 8 n ∣ \geq 81

Divide both sides by

9

∣ 1 + 8 n ∣ \geq 9

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

1 + 8 n \leq - 9 or 1 + 8 n \geq 9

1 + 8 n \leq - 9 or 1 + 8 n \geq 9

n \leq - \frac{5}{4} or n \geq 1

Popular Examples

(5 x - 3)^{2} = 9

x^{2} + 1.5 x - 2.5 = 0

x-1<= 3x+2<= 2x+6

x - 1 \leq 3 x + 2 \leq 2 x + 6

4 x = 8

(3x-4)/6+(2-x)/3 = 1/2

\frac{3 x - 4}{6} + \frac{2 - x}{3} = \frac{1}{2}

Frequently Asked Questions (FAQ)

What is 9|1+8n|-3>= 78 ?
The solution to 9|1+8n|-3>= 78 is n<=-5/4 \lor n>= 1