Solve x+4/2-x-2/4geq2

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

Solve for x

$$x\geq -2$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 2,4. Since 4 is positive, the inequality direction remains the same.

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

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

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

To find the opposite of x-2, find the opposite of each term.

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

The opposite of -2 is 2.

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

Combine 2x and -x to get x.

$$x+8+2\geq 8$$

Add 8 and 2 to get 10.

$$x+10\geq 8$$

Subtract 10 from both sides.

$$x\geq 8-10$$

Subtract 10 from 8 to get -2.

$$x\geq -2$$