Final answer:
The equation to solve is the simplification of a - 3/4 - (a + 5/7) = 5/4. After combining like terms and fractions properly, we find that 'a' is approximately 2.6.
Step-by-step explanation:
To solve the equation for 'a', begin by combining like terms and simplifying. The original equation is:
a - ⅓ - (a + ⅐) = ⅔
First, distribute the negative sign to the terms inside the parenthesis:
a - ⅓ - a - ⅐ = ⅔
Combine like terms by subtracting 'a' from both sides and combining the fractions:
- ⅓ - ⅐ = ⅔
To combine the fractions, find a common denominator which is 28:
-(7/28) - (4/28) = (7/28)
Combine the fractions on the left-hand side:
-(11/28) = (7/28)
Now shift all numerical values to the other side to isolate 'a':
a = ⅓ + ⅐ + ⅔
Convert all fractions to have a common denominator of 28 and then add:
a = 21/28 + 20/28 + 35/28
a = 76/28
Now, simplify the fraction by dividing both numerator and denominator by 4:
a = 19/7
Convert the improper fraction to a mixed number:
a = 2 ⅖
Therefore, rounding to the nearest tenth:
a ≈ 2.6