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

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

Solve for x

$$x>\frac{3}{2}$$

Solution Steps

Use the distributive property to multiply 2 by 4x-1.

$$2x+7<8x-2$$

Subtract 8x from both sides.

$$2x+7-8x<-2$$

Combine 2x and -8x to get -6x.

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

Subtract 7 from both sides.

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

Subtract 7 from -2 to get -9.

$$-6x<-9$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x>\frac{-9}{-6}$$

Reduce the fraction \frac{-9}{-6} to lowest terms by extracting and canceling out -3.

$$x>\frac{3}{2}$$