Question

Solve each of the following equation and check your answer: \[3\left( {x + 2} \right) = 15\]

Answer 1

Hint: Here we are asked to solve the given equation to find the value of \[x\]. This can be done by a simple method called the transposition method that is keeping the unknown variable on one side and moving the other terms to the other side. Then solving that side will give the value of the unknown variable. We are also asked to check the answer so after finding the value of the unknown variable we will substitute it in the given equation to check whether it satisfies the equation or not.

Complete step by step answer:
 It is given that \[3\left( {x + 2} \right) = 15\], we aim to solve this equation to find the value of the unknown variable \[x\]. We are going to use the method called the transposition method. In this method, the unknown variable or the variable that we want to find is kept on one side of the equation alone, then the other variables are transferred to the other side for evaluation. On evaluating this side we will get the value of the unknown variable.
Consider the given equation \[3\left( {x + 2} \right) = 15\], here the unknown variable is \[x\] so, we will try to keep the term \[x\] alone on one side. First, let us take term three to the other side.
\[3\left( {x + 2} \right) = 15 \Rightarrow x + 2 = \dfrac{{15}}{3}\]
On simplifying the above, we get
\[ \Rightarrow x + 2 = 5\]
Now on the left-hand side, we can see that there is an extra term with the unknown variable, transferring that to the other side we get
\[ \Rightarrow x = 5 - 2\]
Simplifying the above equation, we get
\[ \Rightarrow x = 3\]
Thus, we have found the value of the unknown variable \[x\] as \[3\].
Now we have to check whether the answer we found is correct or not. For that, we need to substitute the value of the unknown variable \[x\] in the given equation.
\[3\left( {3 + 2} \right) = 15\]
On simplifying this we get
\[3\left( 5 \right) = 15\]
\[15 = 15\]
Since it satisfies the given equation, the value we found is the correct answer.

Note:
 In the transposition method, when we transfer the terms from one side to the other their operation will change, addition will become subtraction, the subtraction will become an addition, multiplication will become division, and division will become multiplication. Also, the transposition method is more time-efficient than the other available methods to solve a simple equation.