Question

7(-a-3)=3(2a-6) I have the answer but I need help checking it.

Answer 1

Step 1:

In this question, we are meant to solve the following:

`7\text{ ( - a - 3 ) = 3 ( 2a - 6 )}`

Step 2:

Simplifying, we have that:

`\begin{gathered} -7a\text{ - 21 = 6a - 18} \\ \end{gathered}`

collecting like terms, we have that:

`\begin{gathered} -21\text{ + 18 = 6 a + 7a} \\ 13\text{ a = -3} \\ \text{Divide both sides by 13, we have that:} \\ a\text{ = }(-3)/(13) \end{gathered}`

Step 3:

To verify that:

`a\text{ =}(-3)/(13)`

is a solution, we have that:

`7\text{ ( - a - 3 ) = 7 \lbrack -(}(-3)/(13)\text{ ) - 3 \rbrack}`
`7\lbrack\text{ }(3)/(13)\text{ - 3\rbrack = 7 \lbrack }(3)/(13)\text{ - }(39)/(13)\text{ \rbrack = 7 x }(-36)/(13)\text{ = }(-252)/(13)\text{ ( Left Hand Side)}`

Next,

`3\text{ ( 2 a - 6 ) = 3 \lbrack{}2(}(-3)/(13))\text{ - 6 }\rbrack\text{ = 3 \lbrack}(-6)/(13)\text{ - 6\rbrack= 3\lbrack}(-6)/(13)\text{ - }(78)/(13)\rbrack`
`=\text{ 3 \lbrack }(-84)/(13)\text{ \rbrack = }(-252)/(13)\text{ ( Right Hand Side)}`

CONCLUSION:

From the solution and from the verification of the answers, we can see that the correct answer is:

`a\text{ = }\frac{-\text{ 3}}{13}`