Final answer:
The correct answer is option d. – 3. To solve the equation 4 – (⅓(3a+4)) = 7, we distribute the ⅓, combine like fractions, and isolate 'a' by moving terms and simplifying, eventually determining that 'a' equals –3.
Step-by-step explanation:
The correct answer is option d. – 3.
To solve the equation for 'a', we start with the original equation:
4 – (⅓(3a+4)) = 7.
First, distribute the ⅓ into the parentheses:
4 – ((3/5)× 3a + (3/5)× 4) = 7.
Simplify the inside of the parentheses:
4 – ((9/5)a + (12/5)) = 7
Now combine the like terms (The fractions) by converting 4 into a fraction with 5 as denominator:
(20/5) – ((9/5)a + (12/5)) = 7
(20/5) – (9/5)a – (12/5) = 7
(8/5) – (9/5)a = 7
To isolate 'a', move the constant (8/5) to the other side:
–(9/5)a = 7 – (8/5)
–(9/5)a = (35/5) – (8/5)
–(9/5)a = (27/5)
Multiply both sides by –(5/9) to solve for 'a':
a = (27/5) x –(5/9)
a = (27 × 5) / (9 × 5) x –(1)
a = –3