Solve 3x-5/4-x-6/32<1

$$\frac{ 3x-5 }{ 4 } - \frac{ x-6 }{ 32 } < 1$$

Solve for x

$$x<\frac{66}{23}$$

Solution Steps

Multiply both sides of the equation by 32, the least common multiple of 4,32. Since 32 is positive, the inequality direction remains the same.

$$8\left(3x-5\right)-\left(x-6\right)<32$$

Use the distributive property to multiply 8 by 3x-5.

$$24x-40-\left(x-6\right)<32$$

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

$$24x-40-x-\left(-6\right)<32$$

The opposite of -6 is 6.

$$24x-40-x+6<32$$

Combine 24x and -x to get 23x.

$$23x-40+6<32$$

Add -40 and 6 to get -34.

$$23x-34<32$$

Add 34 to both sides.

$$23x<32+34$$

Add 32 and 34 to get 66.

$$23x<66$$

Divide both sides by 23. Since 23 is positive, the inequality direction remains the same.

$$x<\frac{66}{23}$$