Respuesta :
SOLUTION:
Step 1:
In this question, we are meant to solve the following:
[tex]7\text{ ( - a - 3 ) = 3 ( 2a - 6 )}[/tex]Step 2:
Simplifying, we have that:
[tex]\begin{gathered} -7a\text{ - 21 = 6a - 18} \\ \end{gathered}[/tex]collecting like terms, we have that:
[tex]\begin{gathered} -21\text{ + 18 = 6 a + 7a} \\ 13\text{ a = -3} \\ \text{Divide both sides by 13, we have that:} \\ a\text{ = }\frac{-3}{13} \end{gathered}[/tex]Step 3:
To verify that:
[tex]a\text{ =}\frac{-3}{13}[/tex]is a solution, we have that:
[tex]7\text{ ( - a - 3 ) = 7 \lbrack -(}\frac{-3}{13}\text{ ) - 3 \rbrack}[/tex][tex]7\lbrack\text{ }\frac{3}{13}\text{ - 3\rbrack = 7 \lbrack }\frac{3}{13}\text{ - }\frac{39}{13}\text{ \rbrack = 7 x }\frac{-36}{13}\text{ = }\frac{-252}{13}\text{ ( Left Hand Side)}[/tex]Next,
[tex]3\text{ ( 2 a - 6 ) = 3 \lbrack{}2(}\frac{-3}{13})\text{ - 6 }\rbrack\text{ = 3 \lbrack}\frac{-6}{13}\text{ - 6\rbrack= 3\lbrack}\frac{-6}{13}\text{ - }\frac{78}{13}\rbrack[/tex][tex]=\text{ 3 \lbrack }\frac{-84}{13}\text{ \rbrack = }\frac{-252}{13}\text{ ( Right Hand Side)}[/tex]CONCLUSION:
From the solution and from the verification of the answers, we can see that the correct answer is:
[tex]a\text{ = }\frac{-\text{ 3}}{13}[/tex]