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

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

Solve for x

$$x>11$$

Solution Steps

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

$$4\left(2x-\left(x+2\right)\right)>3\left(x+1\right)$$

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

$$4\left(2x-x-2\right)>3\left(x+1\right)$$

Combine 2x and -x to get x.

$$4\left(x-2\right)>3\left(x+1\right)$$

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

$$4x-8>3\left(x+1\right)$$

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

$$4x-8>3x+3$$

Subtract 3x from both sides.

$$4x-8-3x>3$$

Combine 4x and -3x to get x.

$$x-8>3$$

Add 8 to both sides.

$$x>3+8$$

Add 3 and 8 to get 11.

$$x>11$$