Solve x-2/4geqx-1/6+1/12

$$\frac { x - 2 } { 4 } \geq \frac { x - 1 } { 6 } + \frac { 1 } { 12 }$$

Solve for x

$$x\geq 5$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6,12. Since 12 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 3 by x-2.

$$3x-6\geq 2\left(x-1\right)+1$$

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

$$3x-6\geq 2x-2+1$$

Add -2 and 1 to get -1.

$$3x-6\geq 2x-1$$

Subtract 2x from both sides.

$$3x-6-2x\geq -1$$

Combine 3x and -2x to get x.

$$x-6\geq -1$$

Add 6 to both sides.

$$x\geq -1+6$$

Add -1 and 6 to get 5.

$$x\geq 5$$