Solve x+3/3-x-1/6geq1/2

$$\frac { x + 3 } { 3 } - \frac { x - 1 } { 6 } \geq \frac { 1 } { 2 }$$

Solve for x

$$x\geq -4$$

Solution Steps

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

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

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

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

To find the opposite of x-1, find the opposite of each term.

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

The opposite of -1 is 1.

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

Combine 2x and -x to get x.

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

Add 6 and 1 to get 7.

$$x+7\geq 3$$

Subtract 7 from both sides.

$$x\geq 3-7$$

Subtract 7 from 3 to get -4.

$$x\geq -4$$