What is 10-|2x-3|>= 6 ?

The solution to 10-|2x-3|>= 6 is -1/2 <= x<= 7/2

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10-|2x-3|>= 6

10 - ∣ 2 x - 3 ∣ \geq 6

- \frac{1}{2} \leq x \leq \frac{7}{2}

Interval Notation

[- \frac{1}{2}, \frac{7}{2}]

Decimal Notation

- 0.5 \leq x \leq 3.5

Solution steps

10 - ∣ 2 x - 3 ∣ \geq 6

Move

10

to the right side

- ∣ 2 x - 3 ∣ \geq - 4

Multiply both sides by

- 1

∣ 2 x - 3 ∣ \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq 2 x - 3 \leq 4

2 x - 3 \geq - 4 and 2 x - 3 \leq 4

x \geq - \frac{1}{2} and x \leq \frac{7}{2}

Merge Overlapping Intervals

- \frac{1}{2} \leq x \leq \frac{7}{2}

\frac{4 3}{3}

7 (x - 6) = 28

\frac{- 1}{2}

2 x^{2} = 6 x

- 2 x^{4} + 10 x^{3} - 6 x^{2} - 18 x