Solve 4-x/3<x-3/5-1

$$\frac { 4 - x } { 3 } < \frac { x - 3 } { 5 } - 1$$

Solve for x

$$x>\frac{11}{2}$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 3,5. Since 15 is positive, the inequality direction remains the same.

$$5\left(4-x\right)<3\left(x-3\right)-15$$

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

$$20-5x<3\left(x-3\right)-15$$

Use the distributive property to multiply 3 by x-3.

$$20-5x<3x-9-15$$

Subtract 15 from -9 to get -24.

$$20-5x<3x-24$$

Subtract 3x from both sides.

$$20-5x-3x<-24$$

Combine -5x and -3x to get -8x.

$$20-8x<-24$$

Subtract 20 from both sides.

$$-8x<-24-20$$

Subtract 20 from -24 to get -44.

$$-8x<-44$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x>\frac{-44}{-8}$$

Reduce the fraction \frac{-44}{-8} to lowest terms by extracting and canceling out -4.

$$x>\frac{11}{2}$$