Solve x-1/4+2x-1/10<x+2/5+1/2

$$\frac { x - 1 } { 4 } + \frac { 2 x - 1 } { 10 } < \frac { x + 2 } { 5 } + \frac { 1 } { 2 }$$

Solve for x

$$x<5$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,10,5,2. Since 20 is positive, the inequality direction remains the same.

$$5\left(x-1\right)+2\left(2x-1\right)<4\left(x+2\right)+10$$

Use the distributive property to multiply 5 by x-1.

$$5x-5+2\left(2x-1\right)<4\left(x+2\right)+10$$

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

$$5x-5+4x-2<4\left(x+2\right)+10$$

Combine 5x and 4x to get 9x.

$$9x-5-2<4\left(x+2\right)+10$$

Subtract 2 from -5 to get -7.

$$9x-7<4\left(x+2\right)+10$$

Use the distributive property to multiply 4 by x+2.

$$9x-7<4x+8+10$$

Add 8 and 10 to get 18.

$$9x-7<4x+18$$

Subtract 4x from both sides.

$$9x-7-4x<18$$

Combine 9x and -4x to get 5x.

$$5x-7<18$$

Add 7 to both sides.

$$5x<18+7$$

Add 18 and 7 to get 25.

$$5x<25$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x<\frac{25}{5}$$

Divide 25 by 5 to get 5.

$$x<5$$