Solve 3x+2/9-2x+1/3>-1

$$\frac{ 3x+2 }{ 9 } - \frac{ 2x+1 }{ 3 } > -1$$

Solve for x

$$x<\frac{8}{3}$$

Solution Steps

Multiply both sides of the equation by 9, the least common multiple of 9,3. Since 9 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply -3 by 2x+1.

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

Combine 3x and -6x to get -3x.

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

Subtract 3 from 2 to get -1.

$$-3x-1>-9$$

Add 1 to both sides.

$$-3x>-9+1$$

Add -9 and 1 to get -8.

$$-3x>-8$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x<\frac{-8}{-3}$$

Fraction \frac{-8}{-3} can be simplified to \frac{8}{3} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{8}{3}$$