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

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

Solve for x

$$x>3$$

Solution Steps

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

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

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

$$4x-2-\left(x+1\right)>6$$

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

$$4x-2-x-1>6$$

Combine 4x and -x to get 3x.

$$3x-2-1>6$$

Subtract 1 from -2 to get -3.

$$3x-3>6$$

Add 3 to both sides.

$$3x>6+3$$

Add 6 and 3 to get 9.

$$3x>9$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x>\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$x>3$$