Solve 4x+4/3+7x/12>3x+2/4+1

$$\frac{ 4x+4 }{ 3 } + \frac{ 7x }{ 12 } > \frac{ 3x+2 }{ 4 } +1$$

Solve for x

$$x>\frac{1}{7}$$

Solution Steps

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

$$4\left(4x+4\right)+7x>3\left(3x+2\right)+12$$

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

$$16x+16+7x>3\left(3x+2\right)+12$$

Combine 16x and 7x to get 23x.

$$23x+16>3\left(3x+2\right)+12$$

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

$$23x+16>9x+6+12$$

Add 6 and 12 to get 18.

$$23x+16>9x+18$$

Subtract 9x from both sides.

$$23x+16-9x>18$$

Combine 23x and -9x to get 14x.

$$14x+16>18$$

Subtract 16 from both sides.

$$14x>18-16$$

Subtract 16 from 18 to get 2.

$$14x>2$$

Divide both sides by 14. Since 14 is positive, the inequality direction remains the same.

$$x>\frac{2}{14}$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$x>\frac{1}{7}$$