Solve (x-4/2)geq(x-2/3)+(5/6)

$$( \frac { x - 4 } { 2 } ) \geq ( \frac { x - 2 } { 3 } ) + ( \frac { 5 } { 6 } )$$

Solve for x

$$x\geq 13$$

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.

$$3\left(x-4\right)\geq 2\left(x-2\right)+5$$

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

$$3x-12\geq 2\left(x-2\right)+5$$

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

$$3x-12\geq 2x-4+5$$

Add -4 and 5 to get 1.

$$3x-12\geq 2x+1$$

Subtract 2x from both sides.

$$3x-12-2x\geq 1$$

Combine 3x and -2x to get x.

$$x-12\geq 1$$

Add 12 to both sides.

$$x\geq 1+12$$

Add 1 and 12 to get 13.

$$x\geq 13$$