Solve 5x-3/4-3-x/5>2-x/10

$$\frac { 5 x - 3 } { 4 } - \frac { 3 - x } { 5 } > \frac { 2 - x } { 10 }$$

Solve for x

$$x>1$$

Solution Steps

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

$$5\left(5x-3\right)-4\left(3-x\right)>2\left(2-x\right)$$

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

$$25x-15-4\left(3-x\right)>2\left(2-x\right)$$

Use the distributive property to multiply -4 by 3-x.

$$25x-15-12+4x>2\left(2-x\right)$$

Subtract 12 from -15 to get -27.

$$25x-27+4x>2\left(2-x\right)$$

Combine 25x and 4x to get 29x.

$$29x-27>2\left(2-x\right)$$

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

$$29x-27>4-2x$$

Add 2x to both sides.

$$29x-27+2x>4$$

Combine 29x and 2x to get 31x.

$$31x-27>4$$

Add 27 to both sides.

$$31x>4+27$$

Add 4 and 27 to get 31.

$$31x>31$$

Divide both sides by 31. Since 31 is positive, the inequality direction remains the same.

$$x>\frac{31}{31}$$

Divide 31 by 31 to get 1.

$$x>1$$