Solve x/3-x+4/2geq6

$$\frac{ x }{ 3 } - \frac{ x+4 }{ 2 } \geq 6$$

Solve for x

$$x\leq -48$$

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.

$$2x-3\left(x+4\right)\geq 36$$

Use the distributive property to multiply -3 by x+4.

$$2x-3x-12\geq 36$$

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

$$-x-12\geq 36$$

Add 12 to both sides.

$$-x\geq 36+12$$

Add 36 and 12 to get 48.

$$-x\geq 48$$

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

$$x\leq -48$$