Question

How do you solve the linear equation \[\dfrac{15-a}{3}=-9?\]

Answer 1

Hint: We are given an equation as \[\dfrac{15-a}{3}=-9\] and we are asked to solve it. First, we will learn what is known as the solution then we will see what the types of equations we got are. As we will learn that, we have a linear equation then we will find the solution by 2 methods. The first method is called hit and trial and the other is the method involving algebraic tools (+, –, x, /). We will use the second method to solve it. So, first we will begin by multiplying both sides by 3 and then continue further.

Complete step by step solution:
We are given an equation as \[\dfrac{15-a}{3}=-9\] and we can see that it has just one variable and the power of that variable is one only. So, it is a linear equation in one variable.
Now we are asked to find its solution. The solutions are those values which when inserted in the place of the variable will satisfy the equation. The power of the variable will define the possible number of solutions. Since we have power 1, so it can have one solution only.
We can use algebraic operations that are addition, multiplication, division and subtraction to solve this problem. Using these operations, our problem will be easy to solve. Now we have the equation as
\[\dfrac{15-a}{3}=-9\]
On multiplying both the sides by 3, we get,
\[\Rightarrow \left( \dfrac{15-a}{3} \right)\times 3=-9\times 3\]
So, we get,
\[\Rightarrow 15-a=-27\]
Now we will subtract both sides by 15, we get,
\[\Rightarrow 15-a-15=-27-15\]
On simplifying, we get,
\[\Rightarrow -a=-42\]
Now we divide both the sides by – 1, so we get,
\[\Rightarrow \dfrac{-a}{-1}=\dfrac{-42}{-1}\]
So, we get,
\[\Rightarrow a=42\]
Hence the value is a = 42 is the solution.

Note: We can also solve by the method of hit and trial. In this, we use the value of ‘a’ by our assumption and put in the equation at that value that will satisfy the equation and that value is the solution.
Now let us assume a = 30. Putting a = 30 in \[\dfrac{15-a}{3}=-9\] we get,
\[\Rightarrow \dfrac{15-30}{3}=-9\]
\[\Rightarrow \dfrac{-15}{3}=-9\]
On simplifying we get,
\[\Rightarrow -5=-9\]
Which is not true.
So, a = 30 is not the solution.
Now, let us assume a = 36. We will put a = 36 in \[\dfrac{15-a}{3}=-9\] we get,
\[\Rightarrow \dfrac{15-36}{3}=-9\]
\[\Rightarrow \dfrac{-21}{3}=-9\]
On simplifying we get,
\[\Rightarrow -7=-9\]
Which is not true.
So, a = 36 is not the solution.
Now as we can see we are mainly closing towards the solution. So, we will move in the same direction. We will put a = 42 in \[\dfrac{15-a}{3}=-9\] we get,
\[\Rightarrow \dfrac{15-42}{3}=-9\]
\[\Rightarrow -9=-9\]
Hence, this is true. So, a = 42 is the solution.