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

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

Solve for x

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

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.

$$3\left(3x+1\right)-2\left(2x-1\right)>-6$$

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

$$9x+3-2\left(2x-1\right)>-6$$

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

$$9x+3-4x+2>-6$$

Combine 9x and -4x to get 5x.

$$5x+3+2>-6$$

Add 3 and 2 to get 5.

$$5x+5>-6$$

Subtract 5 from both sides.

$$5x>-6-5$$

Subtract 5 from -6 to get -11.

$$5x>-11$$

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

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