Solve 3x+2x(x-3)leq2(5+x^2)

$$3 x + 2 x ( x - 3 ) \leq 2 ( 5 + x ^ { 2 } )$$

Solve for x

$$x\geq -\frac{10}{3}$$

Solution Steps

Use the distributive property to multiply 2x by x-3.

$$3x+2x^{2}-6x\leq 2\left(5+x^{2}\right)$$

Combine 3x and -6x to get -3x.

$$-3x+2x^{2}\leq 2\left(5+x^{2}\right)$$

Use the distributive property to multiply 2 by 5+x^{2}.

$$-3x+2x^{2}\leq 10+2x^{2}$$

Subtract 2x^{2} from both sides.

$$-3x+2x^{2}-2x^{2}\leq 10$$

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

$$-3x\leq 10$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\geq -\frac{10}{3}$$