Solve x+2/5>x-1/4

$$\frac { x + 2 } { 5 } > \frac { x - 1 } { 4 }$$

Solve for x

$$x<13$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 5,4. Since 20 is positive, the inequality direction remains the same.

$$4\left(x+2\right)>5\left(x-1\right)$$

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

$$4x+8>5\left(x-1\right)$$

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

$$4x+8>5x-5$$

Subtract 5x from both sides.

$$4x+8-5x>-5$$

Combine 4x and -5x to get -x.

$$-x+8>-5$$

Subtract 8 from both sides.

$$-x>-5-8$$

Subtract 8 from -5 to get -13.

$$-x>-13$$

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

$$x<\frac{-13}{-1}$$

Fraction \frac{-13}{-1} can be simplified to 13 by removing the negative sign from both the numerator and the denominator.

$$x<13$$