What is 10-3|x-2|>= 4 ?

The solution to 10-3|x-2|>= 4 is 0<= x<= 4

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10-3|x-2|>= 4

10 - 3 ∣ x - 2 ∣ \geq 4

0 \leq x \leq 4

Interval Notation

[0, 4]

Solution steps

10 - 3 ∣ x - 2 ∣ \geq 4

Move

10

to the right side

- 3 ∣ x - 2 ∣ \geq - 6

Multiply both sides by

- 1

3 ∣ x - 2 ∣ \leq 6

Divide both sides by

3

∣ x - 2 ∣ \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq x - 2 \leq 2

x - 2 \geq - 2 and x - 2 \leq 2

x \geq 0 and x \leq 4

Merge Overlapping Intervals

0 \leq x \leq 4

- 1 - x \geq - 15 x - 6 - 3

4 x^{2} - 2 x + 2 - 3 x - x^{2} = 0

6 8 x

364

\frac{1}{1 - x} < 2