Respuesta :
Answer: a = -3
Explanations:
The given equation is:
[tex]4\text{ - }\frac{3}{5}(3a+4)\text{ = 7}[/tex]This can be re-written as:
[tex]4-\frac{3(3a+4)}{5}=7[/tex]Collect like terms:
[tex]\begin{gathered} -\frac{3(3a+4)}{5}=\text{ 7 - 4} \\ -\frac{3(3a+4)}{5}=\text{ 3} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} -3(3a+4)\text{ = 3}\times5 \\ -3(3a+4)=\text{ 15} \\ \text{Expand the bracket} \\ -9a\text{ - 12 = 15} \\ \text{Collect like terms} \\ -9a\text{ = 15 + 12} \\ -9a\text{ = 27} \\ \text{Divide both sides by -9} \\ \frac{-9a}{-9}=\frac{27}{-9} \\ a\text{ = -3} \end{gathered}[/tex]To verify if the solution is correct, substitute a = -3 into the question given. If the Right Hand Side equals the Left Hand Side, then the solution is correct.
[tex]\begin{gathered} 4-\frac{3(3a+4)}{5}=\text{ 7} \\ \text{Substitute a = }-3 \\ 4\text{ - }\frac{3(3(-3)+4)}{5}\text{ = 7} \\ 4\text{ - }\frac{3(-9+4)}{5}\text{ = 7} \\ 4\text{ - }\frac{3(-5)}{5}\text{ = 7} \\ 4\text{ - }\frac{-15}{5}=\text{ 7} \\ 4-(-3)=7 \\ 4+3=7 \\ 7=7 \end{gathered}[/tex]Since the Left Hand Side = Right Hand Side = 7, the solution a = -3 is correct
