Solve x+4/3<2x-6/5

$$\frac { x + 4 } { 3 } < \frac { 2 x - 6 } { 5 }$$

Solve for x

$$x>38$$

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.

$$5\left(x+4\right)<3\left(2x-6\right)$$

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

$$5x+20<3\left(2x-6\right)$$

Use the distributive property to multiply 3 by 2x-6.

$$5x+20<6x-18$$

Subtract 6x from both sides.

$$5x+20-6x<-18$$

Combine 5x and -6x to get -x.

$$-x+20<-18$$

Subtract 20 from both sides.

$$-x<-18-20$$

Subtract 20 from -18 to get -38.

$$-x<-38$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-38}{-1}$$

Fraction \frac{-38}{-1} can be simplified to 38 by removing the negative sign from both the numerator and the denominator.

$$x>38$$