Question

How do you solve the linear equation \[3.3w+5=23\]?

Answer 1

Hint: From the given we have been asked to solve the equation \[3.3w+5=23\]. For solving these questions we will use the basic operations in mathematics which are division and subtraction. Using the basic mathematical operations we will simplify the equation further and solve the given question by finding the value of \[w\].

Complete step-by-step solution:
Firstly, we will take the given equation and we will subtract the integer \[5\] on both the sides of the equation that is from both the left hand side and right hand side of the equation.
So, the equation after subtracting \[5\] will be reduced as follows.
\[\Rightarrow 3.3w+5=23\]
\[\Rightarrow 3.3w+5-5=23-5\]
\[\Rightarrow 3.3w=18\]
Now, to solve the question we have to find the value of \[w\]. In the above simplified equation we have \[3.3w\]. So, for finding the answer we have to further simplify the above equation.
To further simplify the above equation we will use the division operation in mathematics and divide with \[3.3\] on both sides of the equation that is on the left hand side and the right hand side of the equation.
So, we get the equation reduced as follows.
\[\Rightarrow 3.3w=18\]
\[\Rightarrow \dfrac{3.3w}{3.3}=\dfrac{18}{3.3}\]
We will cancel the coefficient of numerator and denominator on the left hand side of the equation.
\[\Rightarrow w=5.\overline{45}=\dfrac{60}{11}\]
Therefore, the solution will be \[\Rightarrow w=5.\overline{45}=\dfrac{60}{11}\].

Note: Students must be very careful in doing the calculations. Students should know how to simplify the given equations and must do the division and subtraction without any mistakes. For example after this step \[\Rightarrow 3.3w+5-5=23-5\] if we write \[\Rightarrow 3.3w=20\] then our solution will be wrong.