Solve 3x-5/4-x-6/12<12

$$\frac{ 3x-5 }{ 4 } - \frac{ x-6 }{ 12 } < 12$$

Solve for x

$$x<\frac{153}{8}$$

Solution Steps

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

$$3\left(3x-5\right)-\left(x-6\right)<144$$

Use the distributive property to multiply 3 by 3x-5.

$$9x-15-\left(x-6\right)<144$$

To find the opposite of x-6, find the opposite of each term.

$$9x-15-x-\left(-6\right)<144$$

The opposite of -6 is 6.

$$9x-15-x+6<144$$

Combine 9x and -x to get 8x.

$$8x-15+6<144$$

Add -15 and 6 to get -9.

$$8x-9<144$$

Add 9 to both sides.

$$8x<144+9$$

Add 144 and 9 to get 153.

$$8x<153$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x<\frac{153}{8}$$