Solve (4)2+x/2geq2x-1/3-2

$$( 4 ) \frac { 2 + x } { 2 } \geq \frac { 2 x - 1 } { 3 } - 2$$

Solve for x

$$x\geq -\frac{19}{4}$$

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.

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

Use the distributive property to multiply 12 by 2+x.

$$24+12x\geq 2\left(2x-1\right)-12$$

Use the distributive property to multiply 2 by 2x-1.

$$24+12x\geq 4x-2-12$$

Subtract 12 from -2 to get -14.

$$24+12x\geq 4x-14$$

Subtract 4x from both sides.

$$24+12x-4x\geq -14$$

Combine 12x and -4x to get 8x.

$$24+8x\geq -14$$

Subtract 24 from both sides.

$$8x\geq -14-24$$

Subtract 24 from -14 to get -38.

$$8x\geq -38$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x\geq \frac{-38}{8}$$

Reduce the fraction \frac{-38}{8} to lowest terms by extracting and canceling out 2.

$$x\geq -\frac{19}{4}$$