Solve -3(4+5x)<-2(7-x)

$$- 3 ( 4 + 5 x ) < - 2 ( 7 - x )$$

Solve for x

$$x>\frac{2}{17}$$

Solution Steps

Use the distributive property to multiply -3 by 4+5x.

$$-12-15x<-2\left(7-x\right)$$

Use the distributive property to multiply -2 by 7-x.

$$-12-15x<-14+2x$$

Subtract 2x from both sides.

$$-12-15x-2x<-14$$

Combine -15x and -2x to get -17x.

$$-12-17x<-14$$

Add 12 to both sides.

$$-17x<-14+12$$

Add -14 and 12 to get -2.

$$-17x<-2$$

Divide both sides by -17. Since -17 is negative, the inequality direction is changed.

$$x>\frac{-2}{-17}$$

Fraction \frac{-2}{-17} can be simplified to \frac{2}{17} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{2}{17}$$