Solve 12+x/2leq7+2/3x

$$12 + \frac { x } { 2 } \leq 7 + \frac { 2 } { 3 } x$$

Solve for x

$$x\geq 30$$

Solution Steps

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

$$72+3x\leq 42+4x$$

Subtract 4x from both sides.

$$72+3x-4x\leq 42$$

Combine 3x and -4x to get -x.

$$72-x\leq 42$$

Subtract 72 from both sides.

$$-x\leq 42-72$$

Subtract 72 from 42 to get -30.

$$-x\leq -30$$

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

$$x\geq \frac{-30}{-1}$$

Fraction \frac{-30}{-1} can be simplified to 30 by removing the negative sign from both the numerator and the denominator.

$$x\geq 30$$