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

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

Solve for x

$$x<31$$

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.

$$4\left(1+2x\right)>3\left(3x-1\right)-24$$

Use the distributive property to multiply 4 by 1+2x.

$$4+8x>3\left(3x-1\right)-24$$

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

$$4+8x>9x-3-24$$

Subtract 24 from -3 to get -27.

$$4+8x>9x-27$$

Subtract 9x from both sides.

$$4+8x-9x>-27$$

Combine 8x and -9x to get -x.

$$4-x>-27$$

Subtract 4 from both sides.

$$-x>-27-4$$

Subtract 4 from -27 to get -31.

$$-x>-31$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<\frac{-31}{-1}$$

Fraction \frac{-31}{-1} can be simplified to 31 by removing the negative sign from both the numerator and the denominator.

$$x<31$$