What is -3|2x-1|+2>=-7 ?

The solution to -3|2x-1|+2>=-7 is -1<= x<= 2

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-3|2x-1|+2>=-7

- 3 ∣ 2 x - 1 ∣ + 2 \geq - 7

- 1 \leq x \leq 2

Interval Notation

[- 1, 2]

Solution steps

- 3 ∣ 2 x - 1 ∣ + 2 \geq - 7

Move

2

to the right side

- 3 ∣ 2 x - 1 ∣ \geq - 9

Multiply both sides by

- 1

3 ∣ 2 x - 1 ∣ \leq 9

Divide both sides by

3

∣ 2 x - 1 ∣ \leq 3

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 3 \leq 2 x - 1 \leq 3

2 x - 1 \geq - 3 and 2 x - 1 \leq 3

x \geq - 1 and x \leq 2

Merge Overlapping Intervals

- 1 \leq x \leq 2

\frac{1}{4} 3

x^{3} + 7 x^{2} - 9 x - 63 > 0

y^{2} (4 - y^{2})

\frac{20 2}{2}

2 (2 x + 3) = - 6 (x + 9)