What is -5|-n+7|>=-45 ?

The solution to -5|-n+7|>=-45 is -2<= n<= 16

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-5|-n+7|>=-45

- 5 ∣ - n + 7 ∣ \geq - 45

- 2 \leq n \leq 16

Interval Notation

[- 2, 16]

Solution steps

- 5 ∣ - n + 7 ∣ \geq - 45

Multiply both sides by

- 1

5 ∣ - n + 7 ∣ \leq 45

Divide both sides by

5

∣ - n + 7 ∣ \leq 9

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 9 \leq - n + 7 \leq 9

- n + 7 \geq - 9 and - n + 7 \leq 9

n \leq 16 and n \geq - 2

Merge Overlapping Intervals

- 2 \leq n \leq 16

\frac{n ^{2} - 14 n + 45}{n ^{2} - 10 n + 9}

4 m - 4 = 4 m

∣ 6 x - 1 ∣ - 10 = 0

\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}}

(3)^{5}