Solve 1+[2x(x-1/2)-(1-x)-2x^2]^3>x+13

$$1 + [ 2 x ( x - \frac { 1 } { 2 } ) - ( 1 - x ) - 2 x ^ { 2 } ] ^ { 3 } > x + 13$$

Solve for x

$$x<-13$$

Solution Steps

Use the distributive property to multiply 2x by x-\frac{1}{2}.

$$1+\left(2x^{2}-x-\left(1-x\right)-2x^{2}\right)^{3}>x+13$$

To find the opposite of 1-x, find the opposite of each term.

$$1+\left(2x^{2}-x-1+x-2x^{2}\right)^{3}>x+13$$

Combine -x and x to get 0.

$$1+\left(2x^{2}-1-2x^{2}\right)^{3}>x+13$$

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

$$1+\left(-1\right)^{3}>x+13$$

Calculate -1 to the power of 3 and get -1.

$$1-1>x+13$$

Subtract 1 from 1 to get 0.

$$0>x+13$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$x+13<0$$

Subtract 13 from both sides. Anything subtracted from zero gives its negation.

$$x<-13$$