Question

How do you solve \[3\left( {x + 1} \right) + 6 = 33\] ?

Answer 1

Hint: We have to find the value of $x$ in the given equation in the question therefore, use the transposition method to solve this question and rearrange the equation such that it becomes easy to solve.

Complete Step by Step Solution:
The equation given to us in the question is \[3\left( {x + 1} \right) + 6 = 33\] , looking at the question, we can conclude that we have to find the value of $x$ in the equation, as it is the only unknown parameter in the equation.
So, to solve this question, we have to make use of the transposition method, this method shifts the number to another side i.e., from left – hand side of the equation to the right – hand side of the equation by changing their function. If the number is to perform the function of addition then, if it shifts to another side changes its role to subtraction while subtraction changes to addition and if the number as to perform the function of multiplication then, after shifting to another side it changes its role to division while division changes to multiplication.
So, the equation given to us is –
\[ \Rightarrow 3\left( {x + 1} \right) + 6 = 33\]
Using the method of transposition and shifting 33 to left – hand side of the equation, we get –
$ \Rightarrow 3\left( {x + 1} \right) + 6 - 33 = 0$
Further solving the equation, we get –
$
   \Rightarrow 3x + 3 + 6 - 33 = 0 \\
   \Rightarrow 3x - 24 = 0 \\
 $
Taking 3 common from the whole equation, we get –
$ \Rightarrow 3\left( {x - 8} \right) = 0$
Now, we know that, if we shift 3 to other side then its function changes to division due to transposition method, then, the above equation can be written as –
$
   \Rightarrow x - 8 = \dfrac{0}{3} \\
   \Rightarrow x - 8 = 0 \\
 $
Now, add and subtract 3 on both sides of the equation, we get –
$ \Rightarrow x = 8$

Hence, the value of $x$ is 8 in the equation \[3\left( {x + 1} \right) + 6 = 33\]

Note:
Students should check whether their answer or the value of $x$ in the given equation is correct or not. To do this, just put the value of $x$ ,which they get in their answer, in the equation given in the question and if both the sides of the equation become equal to each other then, that value of $x$ is correct.