Solve 6-(2x+1)+4(1-x)<7-2x

$$6-(2x+1)+4(1-x) < 7-2x$$

Solve for x

$$x>\frac{1}{2}$$

Solution Steps

To find the opposite of 2x+1, find the opposite of each term.

$$6-2x-1+4\left(1-x\right)<7-2x$$

Subtract 1 from 6 to get 5.

$$5-2x+4\left(1-x\right)<7-2x$$

Use the distributive property to multiply 4 by 1-x.

$$5-2x+4-4x<7-2x$$

Add 5 and 4 to get 9.

$$9-2x-4x<7-2x$$

Combine -2x and -4x to get -6x.

$$9-6x<7-2x$$

Add 2x to both sides.

$$9-6x+2x<7$$

Combine -6x and 2x to get -4x.

$$9-4x<7$$

Subtract 9 from both sides.

$$-4x<7-9$$

Subtract 9 from 7 to get -2.

$$-4x<-2$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x>\frac{-2}{-4}$$

Reduce the fraction \frac{-2}{-4} to lowest terms by extracting and canceling out -2.

$$x>\frac{1}{2}$$