Solve the equation: 6) 7\frac{2}{5} - (x + 1,25) = 2\frac{1}{4}

Task: Solve the equation 7 2/5 - (x + 1.25) = 2 1/4.

Solution:

1. Convert all numbers to fractions:
   • 7 2/5 = (7 * 5 + 2) / 5 = 37/5
   • 1.25 = 125/100 = 5/4
   • 2 1/4 = (2 * 4 + 1) / 4 = 9/4
2. Rewrite the equation with fractions:
   • 37/5 - (x + 5/4) = 9/4
3. Simplify the left side by distributing the negative sign:
   • 37/5 - x - 5/4 = 9/4
4. Isolate the term with 'x':
   • Subtract 37/5 from both sides and add 5/4 to both sides:
   • -x = 9/4 - 37/5 + 5/4
5. Combine like terms (the fractions with denominator 4):
   • -x = (9/4 + 5/4) - 37/5
   • -x = 14/4 - 37/5
   • Simplify 14/4 to 7/2:
   • -x = 7/2 - 37/5
6. Find a common denominator for 2 and 5, which is 10:
   • 7/2 = 35/10
   • 37/5 = 74/10
   • -x = 35/10 - 74/10
   • -x = (35 - 74) / 10
   • -x = -39/10
7. Solve for 'x':
   • Multiply both sides by -1:
   • x = 39/10
8. Convert the improper fraction to a mixed number:
   • x = 3 9/10

Answer: x = 3 9/10