Solve 9/40-1/5x>-5/2(1/10-frac{x-1}{4})

$$\frac { 9 } { 40 } - \frac { 1 } { 5 } x > - \frac { 5 } { 2 } ( \frac { 1 } { 10 } - \frac { x - 1 } { 4 } )$$

Solve for x

$$x<\frac{4}{3}$$

Short Solution Steps

Multiply both sides of the equation by 40, the least common multiple of 40,5,2,10,4. Since 40 is positive, the inequality direction remains the same.

$$9-8x>-100\left(\frac{1}{10}-\frac{x-1}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 4 is 20. Multiply \frac{1}{10} times \frac{2}{2}. Multiply \frac{x-1}{4} times \frac{5}{5}.

$$9-8x>-100\left(\frac{2}{20}-\frac{5\left(x-1\right)}{20}\right)$$

Since \frac{2}{20} and \frac{5\left(x-1\right)}{20} have the same denominator, subtract them by subtracting their numerators.

$$9-8x>-100\times \frac{2-5\left(x-1\right)}{20}$$

Do the multiplications in 2-5\left(x-1\right).

$$9-8x>-100\times \frac{2-5x+5}{20}$$

Combine like terms in 2-5x+5.

$$9-8x>-100\times \frac{7-5x}{20}$$

Cancel out 20, the greatest common factor in 100 and 20.

$$9-8x>-5\left(7-5x\right)$$

Use the distributive property to multiply -5 by 7-5x.

$$9-8x>-35+25x$$

Subtract 25x from both sides.

$$9-8x-25x>-35$$

Combine -8x and -25x to get -33x.

$$9-33x>-35$$

Subtract 9 from both sides.

$$-33x>-35-9$$

Subtract 9 from -35 to get -44.

$$-33x>-44$$

Divide both sides by -33. Since -33 is negative, the inequality direction is changed.

$$x<\frac{-44}{-33}$$

Reduce the fraction \frac{-44}{-33} to lowest terms by extracting and canceling out -11.

$$x<\frac{4}{3}$$