Solve (3x+2)(1-4x)leq-12x^2

$$( 3 x + 2 ) ( 1 - 4 x ) \leq - 12 x ^ { 2 }$$

Solve for x

$$x\geq \frac{2}{5}$$

Solution Steps

Use the distributive property to multiply 3x+2 by 1-4x and combine like terms.

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

Add 12x^{2} to both sides.

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

Combine -12x^{2} and 12x^{2} to get 0.

$$-5x+2\leq 0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-5x\leq -2$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{-2}{-5}$$

Fraction \frac{-2}{-5} can be simplified to \frac{2}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{2}{5}$$