What is 6x^2-5x<= 2x+3 ?

The solution to 6x^2-5x<= 2x+3 is -1/3 <= x<= 3/2

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6x^2-5x<= 2x+3

6 x^{2} - 5 x \leq 2 x + 3

- \frac{1}{3} \leq x \leq \frac{3}{2}

Solution steps

6 x^{2} - 5 x \leq 2 x + 3

Rewrite in standard form

6 x^{2} - 7 x - 3 \leq 0

Factor

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

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

Identify the intervals

- \frac{1}{3} \leq x \leq \frac{3}{2}

5 (x - 6) - 6 (x - 5) = x + 5 - (x - 6)

5 a^{2} - 125

\frac{120}{30}

12 y - 18

2 x^{2} - 13 x + 6