Solve the equation.
-$\frac { 5 - a } { a } + \frac { 3 } { 4 } = \frac { 7 } { a }$
A)-8
B)8
C)-4
D)4

Question

Quizplus · Accepted Answer

To solve the equation $\frac { 5 - a } { a } + \frac { 3 } { 4 } = \frac { 7 } { a }$, first find a common denominator for the fractions, which is $a$. The equation becomes $\frac { 5 - a } { a } + \frac { 3a } { 4a } = \frac { 7 } { a }$. Simplifying, we get $\frac { 5 - a + 3a } { 4a } = \frac { 7 } { a }$, which simplifies to $\frac { 5 + 2a } { 4a } = \frac { 7 } { a }$. Multiplying both sides by $4a$ to eliminate the denominator gives $5 + 2a = 28$. Subtracting 5 from both sides gives $2a = 23$, which is incorrect upon review. Correctly, after simplifying the initial equation, we should directly compare the numerators since the denominators are equal, leading to $5 - a + \frac{3a}{4} = 7$. Multiplying everything by 4 to clear the fraction: $20 - 4a + 3a = 28$. Simplifying gives $-a = 8$, so $a = -8$.

Solve the Equation 5−aa+34=7a\frac { 5 - a } { a } + \frac { 3 } { 4 } = \frac { 7 } { a }a5−a​+43​=a7​

Solve the Equation $\frac { 5 - a } { a } + \frac { 3 } { 4 } = \frac { 7 } { a }$