Question

How do you solve \[3a-7=7a-3\]?

Answer 1

Hint: In this problem, we have to solve and find the value of a. we can first set the numbers with variables to one side and the remaining other terms to the other side. We can first subtract 7a on both sides, then we can add 7 on both sides to get an equation which we can simplify. We can then simplify the resulting equation to get the value of a.

Complete step by step answer:
We know that the equation given to be solved is,
\[3a-7=7a-3\]
We can first subtract 7a on both the left-hand side and the right-hand side in the equation, we get
\[\Rightarrow 3a-7a-7=-3\]
we can add 7 on both sides to get an equation which we can simplify.
\[\Rightarrow 3a-7a=-3+7\]
Now we have an equation which we can simplify as we have similar terms on both sides.
We can simplify the above step, we get
\[\Rightarrow -4a=4\]
Now we can divide the number 4 on both sides, we get
\[\Rightarrow -a=1\]
Now we can multiply -1 on both sides, we get
\[\Rightarrow a=-1\]
Therefore, the value of a is -1.

Note:
Students male mistakes while adding or subtracting the correct numbers in the left-hand side and the right-hand side in the equation to take the terms with variables to one side and the remaining other terms to the other side. We can substitute the resulting value in the given equation to check whether the value is correct.
We can substitute -1 in the given equation, we get
\[\begin{align}
  & \Rightarrow 3\left( -1 \right)-7=7\left( -1 \right)-3 \\
 & \Rightarrow 3+7=7+3 \\
 & \Rightarrow 10=10 \\
\end{align}\]
Therefore, the value is a = -1.