Solve x+2/2+x-2/3+x-1/4geq3+x/2

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

Solve for x

$$x\geq 5$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,3,4. Since 12 is positive, the inequality direction remains the same.

$$6\left(x+2\right)+4\left(x-2\right)+3\left(x-1\right)\geq 36+6x$$

Use the distributive property to multiply 6 by x+2.

$$6x+12+4\left(x-2\right)+3\left(x-1\right)\geq 36+6x$$

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

$$6x+12+4x-8+3\left(x-1\right)\geq 36+6x$$

Combine 6x and 4x to get 10x.

$$10x+12-8+3\left(x-1\right)\geq 36+6x$$

Subtract 8 from 12 to get 4.

$$10x+4+3\left(x-1\right)\geq 36+6x$$

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

$$10x+4+3x-3\geq 36+6x$$

Combine 10x and 3x to get 13x.

$$13x+4-3\geq 36+6x$$

Subtract 3 from 4 to get 1.

$$13x+1\geq 36+6x$$

Subtract 6x from both sides.

$$13x+1-6x\geq 36$$

Combine 13x and -6x to get 7x.

$$7x+1\geq 36$$

Subtract 1 from both sides.

$$7x\geq 36-1$$

Subtract 1 from 36 to get 35.

$$7x\geq 35$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x\geq \frac{35}{7}$$

Divide 35 by 7 to get 5.

$$x\geq 5$$