Solve x+1/5-x-2/2geq0

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

Solve for x

$$x\leq 4$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 2 by x+1.

$$2x+2-5\left(x-2\right)\geq 0$$

Use the distributive property to multiply -5 by x-2.

$$2x+2-5x+10\geq 0$$

Combine 2x and -5x to get -3x.

$$-3x+2+10\geq 0$$

Add 2 and 10 to get 12.

$$-3x+12\geq 0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-3x\geq -12$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{-12}{-3}$$

Divide -12 by -3 to get 4.

$$x\leq 4$$