Solve -2(x-4)<5(x-1)

$$- 2 ( x - 4 ) < 5 ( x - 1 )$$

Solve for x

$$x>\frac{13}{7}$$

Solution Steps

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

$$-2x+8<5\left(x-1\right)$$

Use the distributive property to multiply 5 by x-1.

$$-2x+8<5x-5$$

Subtract 5x from both sides.

$$-2x+8-5x<-5$$

Combine -2x and -5x to get -7x.

$$-7x+8<-5$$

Subtract 8 from both sides.

$$-7x<-5-8$$

Subtract 8 from -5 to get -13.

$$-7x<-13$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x>\frac{-13}{-7}$$

Fraction \frac{-13}{-7} can be simplified to \frac{13}{7} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{13}{7}$$