n-3/4+n+57=5/14
2n=5/14+3/4-57
2n=-55
n=-55/2= -27.5
To solve the equation (n - 3/4) + (n + 57) = 5/14, you will need to simplify and isolate the variable (n).
Step 1: Distribute the addition to remove parentheses:
n - 3/4 + n + 57 = 5/14
This becomes:
2n - 3/4 + 57 = 5/14
Step 2: Combine like terms:
2n + 57 - 3/4 = 5/14
Step 3: Convert mixed numbers to improper fractions:
2n + 57 - 3/4 = 5/14
Multiplying the denominator (4) by the whole number (57) gives us:
2n + (4*57)/4 - 3/4 = 5/14
2n + 228/4 - 3/4 = 5/14
This simplifies to:
2n + 225/4 = 5/14
Step 4: Taking the common denominator:
Since the denominators are different (4 and 14), you need to find a common multiple, which in this case is 28. Multiply both sides of the equation by 28 to eliminate the fractions:
28 * (2n + 225/4) = 28 * (5/14)
56n + 225 * 7 = 140 * 5
56n + 1575 = 700
Step 5: Isolate the variable:
Next, subtract 1575 from both sides of the equation:
56n + 1575 - 1575 = 700 - 1575
56n = -875
Step 6: Solve for n:
Finally, divide both sides of the equation by 56 to solve for n:
n = -875 / 56
To get the exact or simplified answer, divide the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of -875 and 56 is 7:
n = -125 / 8
So, the solution to the equation (n - 3/4) + (n + 57) = 5/14 is n = -125/8.