Solve x-2/5-x-1/4>x-3/2-1

$$\frac{ x-2 }{ 5 } - \frac{ x-1 }{ 4 } > \frac{ x-3 }{ 2 } -1$$

Solve for x

$$x<\frac{47}{11}$$

Solution Steps

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

$$4\left(x-2\right)-5\left(x-1\right)>10\left(x-3\right)-20$$

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

$$4x-8-5\left(x-1\right)>10\left(x-3\right)-20$$

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

$$4x-8-5x+5>10\left(x-3\right)-20$$

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

$$-x-8+5>10\left(x-3\right)-20$$

Add -8 and 5 to get -3.

$$-x-3>10\left(x-3\right)-20$$

Use the distributive property to multiply 10 by x-3.

$$-x-3>10x-30-20$$

Subtract 20 from -30 to get -50.

$$-x-3>10x-50$$

Subtract 10x from both sides.

$$-x-3-10x>-50$$

Combine -x and -10x to get -11x.

$$-11x-3>-50$$

Add 3 to both sides.

$$-11x>-50+3$$

Add -50 and 3 to get -47.

$$-11x>-47$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x<\frac{-47}{-11}$$

Fraction \frac{-47}{-11} can be simplified to \frac{47}{11} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{47}{11}$$