Solve 2x+1/3-1>3x-8/2+2

$$\frac { 2 x + 1 } { 3 } - 1 > \frac { 3 x - 8 } { 2 } + 2$$

Solve for x

$$x<\frac{8}{5}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(2x+1\right)-6>3\left(3x-8\right)+12$$

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

$$4x+2-6>3\left(3x-8\right)+12$$

Subtract 6 from 2 to get -4.

$$4x-4>3\left(3x-8\right)+12$$

Use the distributive property to multiply 3 by 3x-8.

$$4x-4>9x-24+12$$

Add -24 and 12 to get -12.

$$4x-4>9x-12$$

Subtract 9x from both sides.

$$4x-4-9x>-12$$

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

$$-5x-4>-12$$

Add 4 to both sides.

$$-5x>-12+4$$

Add -12 and 4 to get -8.

$$-5x>-8$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x<\frac{-8}{-5}$$

Fraction \frac{-8}{-5} can be simplified to \frac{8}{5} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{8}{5}$$