Solve 5-x/2-x-17/4>=x/3-7x-3/12

$$\frac{ 5-x }{ 2 } - \frac{ x-17 }{ 4 } > = \frac{ x }{ 3 } - \frac{ 7x-3 }{ 12 }$$

Solve for x

$$x<13$$

Solution Steps

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

$$6\left(5-x\right)-3\left(x-17\right)>4x-\left(7x-3\right)$$

Use the distributive property to multiply 6 by 5-x.

$$30-6x-3\left(x-17\right)>4x-\left(7x-3\right)$$

Use the distributive property to multiply -3 by x-17.

$$30-6x-3x+51>4x-\left(7x-3\right)$$

Combine -6x and -3x to get -9x.

$$30-9x+51>4x-\left(7x-3\right)$$

Add 30 and 51 to get 81.

$$81-9x>4x-\left(7x-3\right)$$

To find the opposite of 7x-3, find the opposite of each term.

$$81-9x>4x-7x-\left(-3\right)$$

The opposite of -3 is 3.

$$81-9x>4x-7x+3$$

Combine 4x and -7x to get -3x.

$$81-9x>-3x+3$$

Add 3x to both sides.

$$81-9x+3x>3$$

Combine -9x and 3x to get -6x.

$$81-6x>3$$

Subtract 81 from both sides.

$$-6x>3-81$$

Subtract 81 from 3 to get -78.

$$-6x>-78$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x<\frac{-78}{-6}$$

Divide -78 by -6 to get 13.

$$x<13$$