Solve 2x(x-3)geq3(1-3x)+2x^2+2x

$$2 x ( x - 3 ) \geq 3 ( 1 - 3 x ) + 2 x ^ { 2 } + 2 x$$

Solve for x

$$x\geq 3$$

Solution Steps

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

$$2x^{2}-6x\geq 3\left(1-3x\right)+2x^{2}+2x$$

Use the distributive property to multiply 3 by 1-3x.

$$2x^{2}-6x\geq 3-9x+2x^{2}+2x$$

Combine -9x and 2x to get -7x.

$$2x^{2}-6x\geq 3-7x+2x^{2}$$

Add 7x to both sides.

$$2x^{2}-6x+7x\geq 3+2x^{2}$$

Combine -6x and 7x to get x.

$$2x^{2}+x\geq 3+2x^{2}$$

Subtract 2x^{2} from both sides.

$$2x^{2}+x-2x^{2}\geq 3$$

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

$$x\geq 3$$