What is 6x^2-4x-2<= 9x^2-15x+6 ?

The solution to 6x^2-4x-2 = 8/3

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6x^2-4x-2<= 9x^2-15x+6

6 x^{2} - 4 x - 2 \leq 9 x^{2} - 15 x + 6

x \leq 1 or x \geq \frac{8}{3}

Interval Notation

(- \infty, 1] \cup [\frac{8}{3}, \infty)

Decimal Notation

x \leq 1 or x \geq 2.66666 \dots

Solution steps

6 x^{2} - 4 x - 2 \leq 9 x^{2} - 15 x + 6

Rewrite in standard form

- 3 x^{2} + 11 x - 8 \leq 0

Factor

- 3 x^{2} + 11 x - 8 : - (x - 1) (3 x - 8)

- (x - 1) (3 x - 8) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 1) (3 x - 8)) (- 1) \geq 0 \cdot (- 1)

Simplify

(x - 1) (3 x - 8) \geq 0

Identify the intervals

x \leq 1 or x \geq \frac{8}{3}

(4 x^{- 4})^{- \frac{1}{2}}

1 + \frac{21000000}{49000000}

5 x = 1 - 3 x^{2}

2 (\frac{2}{3})^{2} + 5 (\frac{2}{3}) + 6

∣ 2 x + 1 ∣ < 3

What is 6x^2-4x-2<= 9x^2-15x+6 ?
The solution to 6x^2-4x-2<= 9x^2-15x+6 is x<= 1\lor x>= 8/3