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

The solution to -2|x-3|>=-4 is 1<= x<= 5

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-2|x-3|>=-4

- 2 ∣ x - 3 ∣ \geq - 4

1 \leq x \leq 5

Interval Notation

[1, 5]

Solution steps

- 2 ∣ x - 3 ∣ \geq - 4

Multiply both sides by

- 1

2 ∣ x - 3 ∣ \leq 4

Divide both sides by

2

∣ x - 3 ∣ \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq x - 3 \leq 2

x - 3 \geq - 2 and x - 3 \leq 2

x \geq 1 and x \leq 5

Merge Overlapping Intervals

1 \leq x \leq 5

\frac{3 x - 1}{4} = 5

- 12 x \leq - 94 + 85 x

3 z^{2} - 2 z - 5

\frac{1}{2} (14)

4 x^{2} - 3 = - 4 + 7 x