d. (7-2 x)/(2)-(2)/(5)(2-x)=1 (1)/(4)

To solve the equation \(\frac{7-2x}{2} - \frac{2}{5}(2-x) = 1\frac{1}{4}\), follow these steps:<br /><br />1. Convert the mixed number to an improper fraction:<br /> \[<br /> 1\frac{1}{4} = \frac{5}{4}<br /> \]<br /><br />2. Rewrite the equation with the improper fraction:<br /> \[<br /> \frac{7-2x}{2} - \frac{2}{5}(2-x) = \frac{5}{4}<br /> \]<br /><br />3. Find a common denominator for all fractions involved. The least common multiple of 2, 5, and 4 is 20.<br /><br />4. Rewrite each fraction with the common denominator of 20:<br /> \[<br /> \frac{7-2x}{2} = \frac{10(7-2x)}{20} = \frac{70-20x}{20}<br /> \]<br /> \[<br /> \frac{2}{5}(2-x) = \frac{4(2-x)}{20} = \frac{8-4x}{20}<br /> \]<br /> \[<br /> \frac{5}{4} = \frac{25}{20}<br /> \]<br /><br />5. Substitute these back into the equation:<br /> \[<br /> \frac{70-20x}{20} - \frac{8-4x}{20} = \frac{25}{20}<br /> \]<br /><br />6. Combine the fractions on the left side:<br /> \[<br /> \frac{70-20x - (8-4x)}{20} = \frac{25}{20}<br /> \]<br /> \[<br /> \frac{70-20x - 8 + 4x}{20} = \frac{25}{20}<br /> \]<br /> \[<br /> \frac{62-16x}{20} = \frac{25}{20}<br /> \]<br /><br />7. Since the denominators are equal, set the numerators equal to each other:<br /> \[<br /> 62 - 16x = 25<br /> \]<br /><br />8. Solve for \(x\):<br /> \[<br /> 62 - 25 = 16x<br /> \]<br /> \[<br /> 37 = 16x<br /> \]<br /> \[<br /> x = \frac{37}{16}<br /> \]<br /><br />Therefore, the solution to the equation is:<br />\[<br />x = \frac{37}{16}<br />\]