What is -12x^2+5x+7<= 5 ?

The solution to -12x^2+5x+7 = 2/3

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-12x^2+5x+7<= 5

- 12 x^{2} + 5 x + 7 \leq 5

x \leq - \frac{1}{4} or x \geq \frac{2}{3}

Interval Notation

(- \infty, - \frac{1}{4}] \cup [\frac{2}{3}, \infty)

Decimal Notation

x \leq - 0.25 or x \geq 0.66666 \dots

Solution steps

- 12 x^{2} + 5 x + 7 \leq 5

Rewrite in standard form

- 12 x^{2} + 5 x + 2 \leq 0

Factor

- 12 x^{2} + 5 x + 2 : - (4 x + 1) (3 x - 2)

- (4 x + 1) (3 x - 2) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (4 x + 1) (3 x - 2)) (- 1) \geq 0 \cdot (- 1)

Simplify

(4 x + 1) (3 x - 2) \geq 0

Identify the intervals

x \leq - \frac{1}{4} or x \geq \frac{2}{3}

r - 11 = 5

7 a x - 21 x + 12 - 4 a + 4 x y - 6 y + 15 - 10 x

5 (x + 1) - 4 x \geq - 9

2 x^{2} - 7 x < - 5

\frac{3}{4} x - 2 = \frac{2}{5}

What is -12x^2+5x+7<= 5 ?
The solution to -12x^2+5x+7<= 5 is x<=-1/4 \lor x>= 2/3