Question

How do you solve \[3a + \left( {2a - 5} \right) = 13 - 2\left( {a + 2} \right)\] ?

Answer 1

Hint: We are given with an expression and we need to find the value of $a$. We need to rearrange or alter the given equation. For that first, we have to separate the variables from the numbers by transferring it to the other side. Then, we have to solve the given problem by using the basic mathematical operations and transferring methods for solving the given equations.

Complete step-by-step solution:
In this question the given equation is \[3a + \left( {2a - 5} \right) = 13 - 2\left( {a + 2} \right)\], we need to find the value of the variable.
\[ \Rightarrow 3a + \left( {2a - 5} \right) = 13 - 2\left( {a + 2} \right)\]
Multiplying the brackets we get
\[ \Rightarrow 3a + 2a - 5 = 13 - 2a - 4\]
Further solving it,
$ \Rightarrow 5a - 5 = 13 - 4 - 2a$
$ \Rightarrow 5a - 5 = 9 - 2a$
First, we have to transfer the numbers or the coefficients’ to one side. When transferring any variable or numbers to the other side, the signs of the same will be changed to its opposite sign.
Here, $5a - 5 = 9 - 2a$
$ \Rightarrow 5a + 2a = 9 + 5$
Adding$2a$ and $5a$ on the left hand side, we get
$ \Rightarrow 7a = 9 + 5$
Adding $9$ and $5$ on the right hand side, we get
\[ \Rightarrow 7a = 14\]
Transferring the $7$ to the other side, we get
$ \Rightarrow a = \frac{{14}}{7}$
We are dividing $7$ because, in the left hand side $7$ was multiplied to $a$, so in order to find $a$ we need to divide it by $7$

Therefore, the required answer is $a = 2$.

Note: After getting the answer, always apply the value of the variable in the given equation to check it whether the answer obtained is correct or not.
If this type of questions are asked in MCQ type, you can save your time by directly applying the given choices in the place of $a$ and check whether the equation satisfies them.
For example, assume that for this question they have given choices like,
Find $a$, $7a = 9 + 5$.
${\text{a) 1}}$ ${\text{b) - 3}}$${\text{c) 2}}$
You can directly substitute the values in$7a = 9 + 5$ and check,
If $a = 1$ the equation is not satisfied
If $a = - 3$ the equation is not satisfied
If $a = 2$, the equation is satisfied.
Therefore ${\text{c) 2}}$ is the correct answer.