What is |x^2-4|<=-2x+4 ?

The solution to |x^2-4|<=-2x+4 is -4<= x<= 0\lor x=2

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|x^2-4|<=-2x+4

x^{2} - 4 \leq - 2 x + 4

- 4 \leq x \leq 0 or x = 2

Interval Notation

[- 4, 0] \cup x = 2

Solution steps

x^{2} - 4 \leq - 2 x + 4

Find positive and negative intervals

x \leq - 2, - 2 < x < 2, x \geq 2

Solve the inequality for each interval

- 4 \leq x \leq - 2 or - 2 < x \leq 0 or x = 2

Merge Overlapping Intervals

- 4 \leq x \leq 0 or x = 2

- 2 (8 k - 24) \geq - 12

\frac{5}{26}

\frac{1}{5 ^{- 1}}

\frac{0}{3}

- 9 > 2 x - 8 > 3