Solve (2x+1)(x-5)leq2(x+2)(x-4)

$$( 2 x + 1 ) ( x - 5 ) \leq 2 ( x + 2 ) ( x - 4 )$$

Solve for x

$$x\geq \frac{11}{5}$$

Solution Steps

Use the distributive property to multiply 2x+1 by x-5 and combine like terms.

$$2x^{2}-9x-5\leq 2\left(x+2\right)\left(x-4\right)$$

Use the distributive property to multiply 2 by x+2.

$$2x^{2}-9x-5\leq \left(2x+4\right)\left(x-4\right)$$

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

$$2x^{2}-9x-5\leq 2x^{2}-4x-16$$

Subtract 2x^{2} from both sides.

$$2x^{2}-9x-5-2x^{2}\leq -4x-16$$

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

$$-9x-5\leq -4x-16$$

Add 4x to both sides.

$$-9x-5+4x\leq -16$$

Combine -9x and 4x to get -5x.

$$-5x-5\leq -16$$

Add 5 to both sides.

$$-5x\leq -16+5$$

Add -16 and 5 to get -11.

$$-5x\leq -11$$

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

$$x\geq \frac{-11}{-5}$$

Fraction \frac{-11}{-5} can be simplified to \frac{11}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{11}{5}$$