What is 3x^2-5x>= 4x^2+6 ?

The solution to 3x^2-5x>= 4x^2+6 is -3<= x<=-2

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3x^2-5x>= 4x^2+6

3 x^{2} - 5 x \geq 4 x^{2} + 6

- 3 \leq x \leq - 2

Interval Notation

[- 3, - 2]

Solution steps

3 x^{2} - 5 x \geq 4 x^{2} + 6

Rewrite in standard form

- x^{2} - 5 x - 6 \geq 0

Factor

- x^{2} - 5 x - 6 : - (x + 2) (x + 3)

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

- 3 \leq x \leq - 2

5 (x - 3) + 4 (x + 3) = 3 (x - 1)

9 c + 18 = 27 - 3 c

37 = g + 18

\frac{- 1}{- 2}

7 - \frac{6}{5 - \frac{4}{3 - \frac{1}{2}}}