Solve x+2/5-x-1/4leq0

$$\frac { x + 2 } { 5 } - \frac { x - 1 } { 4 } \leq 0$$

Solve for x

$$x\geq 13$$

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.

$$4\left(x+2\right)-5\left(x-1\right)\leq 0$$

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

$$4x+8-5\left(x-1\right)\leq 0$$

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

$$4x+8-5x+5\leq 0$$

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

$$-x+8+5\leq 0$$

Add 8 and 5 to get 13.

$$-x+13\leq 0$$

Subtract 13 from both sides. Anything subtracted from zero gives its negation.

$$-x\leq -13$$

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

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

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

$$x\geq 13$$