Solve x-6/2geqx-2/3+5/6

$$\frac { x - 6 } { 2 } \geq \frac { x - 2 } { 3 } + \frac { 5 } { 6 }$$

Solve for x

$$x\geq 19$$

Solution Steps

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

$$3\left(x-6\right)\geq 2\left(x-2\right)+5$$

Use the distributive property to multiply 3 by x-6.

$$3x-18\geq 2\left(x-2\right)+5$$

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

$$3x-18\geq 2x-4+5$$

Add -4 and 5 to get 1.

$$3x-18\geq 2x+1$$

Subtract 2x from both sides.

$$3x-18-2x\geq 1$$

Combine 3x and -2x to get x.

$$x-18\geq 1$$

Add 18 to both sides.

$$x\geq 1+18$$

Add 1 and 18 to get 19.

$$x\geq 19$$