What is 2-5|10-2n|>=-28 ?

The solution to 2-5|10-2n|>=-28 is 2<= n<= 8

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2-5|10-2n|>=-28

2 - 5 ∣ 10 - 2 n ∣ \geq - 28

2 \leq n \leq 8

Interval Notation

[2, 8]

Solution steps

2 - 5 ∣ 10 - 2 n ∣ \geq - 28

Move

2

to the right side

- 5 ∣ 10 - 2 n ∣ \geq - 30

Multiply both sides by

- 1

5 ∣ 10 - 2 n ∣ \leq 30

Divide both sides by

5

∣ 10 - 2 n ∣ \leq 6

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 6 \leq 10 - 2 n \leq 6

10 - 2 n \geq - 6 and 10 - 2 n \leq 6

n \leq 8 and n \geq 2

Merge Overlapping Intervals

2 \leq n \leq 8

\frac{x}{3} + \frac{x}{7} \geq 7

4 - 3 x \leq - 8

(6 + 3)^{2}

n^{2} + 2 n + 1 = 0

\frac{4 x - 6}{10} + 2 x = 21 - \frac{3 ( x + 1 )}{12}