Solve x-2/4+2/3geqx-4/6

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

Solve for x

$$x\geq -10$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3,6. Since 12 is positive, the inequality direction remains the same.

$$3\left(x-2\right)+8\geq 2\left(x-4\right)$$

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

$$3x-6+8\geq 2\left(x-4\right)$$

Add -6 and 8 to get 2.

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

Use the distributive property to multiply 2 by x-4.

$$3x+2\geq 2x-8$$

Subtract 2x from both sides.

$$3x+2-2x\geq -8$$

Combine 3x and -2x to get x.

$$x+2\geq -8$$

Subtract 2 from both sides.

$$x\geq -8-2$$

Subtract 2 from -8 to get -10.

$$x\geq -10$$