Solve 3x-1/4--x-1/2<9x+4/8

$$\frac { 3 x - 1 } { 4 } - \frac { - x - 1 } { 2 } < \frac { 9 x + 4 } { 8 }$$

Solve for x

$$x<2$$

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 4,2,8. Since 8 is positive, the inequality direction remains the same.

$$2\left(3x-1\right)-4\left(-x-1\right)<9x+4$$

Use the distributive property to multiply 2 by 3x-1.

$$6x-2-4\left(-x-1\right)<9x+4$$

Use the distributive property to multiply -4 by -x-1.

$$6x-2-4\left(-x\right)+4<9x+4$$

Multiply -4 and -1 to get 4.

$$6x-2+4x+4<9x+4$$

Combine 6x and 4x to get 10x.

$$10x-2+4<9x+4$$

Add -2 and 4 to get 2.

$$10x+2<9x+4$$

Subtract 9x from both sides.

$$10x+2-9x<4$$

Combine 10x and -9x to get x.

$$x+2<4$$

Subtract 2 from both sides.

$$x<4-2$$

Subtract 2 from 4 to get 2.

$$x<2$$