Solve 1/3(x-6)geqx/2-1

$$\frac { 1 } { 3 } ( x - 6 ) \geq \frac { x } { 2 } - 1$$

Solve for x

$$x\leq -6$$

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.

$$2\left(x-6\right)\geq 3x-6$$

Use the distributive property to multiply 2 by x-6.

$$2x-12\geq 3x-6$$

Subtract 3x from both sides.

$$2x-12-3x\geq -6$$

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

$$-x-12\geq -6$$

Add 12 to both sides.

$$-x\geq -6+12$$

Add -6 and 12 to get 6.

$$-x\geq 6$$

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

$$x\leq -6$$