Solve 1+x+1/2geq2-x+7/3

$$1 + \frac { x + 1 } { 2 } \geq 2 - \frac { x + 7 } { 3 }$$

Solve for x

$$x\geq -\frac{11}{5}$$

Solution Steps

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

$$6+3\left(x+1\right)\geq 12-2\left(x+7\right)$$

Use the distributive property to multiply 3 by x+1.

$$6+3x+3\geq 12-2\left(x+7\right)$$

Add 6 and 3 to get 9.

$$9+3x\geq 12-2\left(x+7\right)$$

Use the distributive property to multiply -2 by x+7.

$$9+3x\geq 12-2x-14$$

Subtract 14 from 12 to get -2.

$$9+3x\geq -2-2x$$

Add 2x to both sides.

$$9+3x+2x\geq -2$$

Combine 3x and 2x to get 5x.

$$9+5x\geq -2$$

Subtract 9 from both sides.

$$5x\geq -2-9$$

Subtract 9 from -2 to get -11.

$$5x\geq -11$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x\geq -\frac{11}{5}$$