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

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

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

x \leq - \frac{7}{3} or x \geq 1

Solution steps

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

Rewrite in standard form

- 3 x^{2} - 4 x + 7 \leq 0

Factor

- 3 x^{2} - 4 x + 7 : - (x - 1) (3 x + 7)

- (x - 1) (3 x + 7) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 1) (3 x + 7)) (- 1) \geq 0 \cdot (- 1)

Simplify

(x - 1) (3 x + 7) \geq 0

Identify the intervals

x \leq - \frac{7}{3} or x \geq 1

4 x^{2} = 3 x

\frac{x ^{2} - 1}{2} - 11 x = 11

\frac{x + 2}{- 5} > 10

(3 p)^{2}

\frac{( 8 0 ^{10} )}{( 8 0 ^{9} )}

What is 6x^2-4x-2<= 9x^2-15+6 ?
The solution to 6x^2-4x-2<= 9x^2-15+6 is x<=-7/3 \lor x>= 1