Solve 2x+5/3-1/2>1div4x+2/6

$$\frac{ 2x+5 }{ 3 } - \frac{ 1 }{ 2 } > 1 \div 4x+ \frac{ 2 }{ 6 }$$

Solve for x

$$x>-2$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,2,4,6. Since 12 is positive, the inequality direction remains the same.

$$4\left(2x+5\right)-6>3x+2\times 2$$

Use the distributive property to multiply 4 by 2x+5.

$$8x+20-6>3x+2\times 2$$

Subtract 6 from 20 to get 14.

$$8x+14>3x+2\times 2$$

Multiply 2 and 2 to get 4.

$$8x+14>3x+4$$

Subtract 3x from both sides.

$$8x+14-3x>4$$

Combine 8x and -3x to get 5x.

$$5x+14>4$$

Subtract 14 from both sides.

$$5x>4-14$$

Subtract 14 from 4 to get -10.

$$5x>-10$$

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

$$x>\frac{-10}{5}$$

Divide -10 by 5 to get -2.

$$x>-2$$