Solve x+1/3geqx/2

$$\frac { x + 1 } { 3 } \geq \frac { x } { 2 }$$

Solve for x

$$x\leq 2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(x+1\right)\geq 3x$$

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

$$2x+2\geq 3x$$

Subtract 3x from both sides.

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

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

$$-x+2\geq 0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-x\geq -2$$

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

$$x\leq \frac{-2}{-1}$$

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$x\leq 2$$