Question

How do you solve $\dfrac{3w+8}{2}=25$ ?

Answer 1

We are given equation as $\dfrac{3w+8}{2}=25$ , we will learn what type of equation it is, then we will learn what are the solution of a equation means then after that we will try the method of hit and trial to look for the value which will satisfy the given equation. we will also learn how arithmetic tools may be to solve our problem.

Complete step by step solution:
We are given an equation as $\dfrac{3w+8}{2}=25$ , we can see that our equation consists of just variables and the highest power is 1, so it means we have a linear equation in 1 variable.
Now we learn about solutions, solutions of any equation are those values which will satisfy our equation. a linear equation can have at most one solution.
Now to find the solution we will use the method of hit and trial, in this method, we try the value of which may suit the equation.
So, we let $w=1$ .
We put $w=1$ in $\dfrac{3w+8}{2}=25$ , we get –
$\Rightarrow \dfrac{3\times 1+8}{2}=25$
By simplifying, we get –
$\Rightarrow \dfrac{11}{2}=25$
Which is not true.
So, $w=1$ is not the solution.
So, we let $w=5$ .
We put $w=5$ in $\dfrac{3w+8}{2}=25$ .
We get –
$\Rightarrow \dfrac{3\times 5+8}{2}=25$ .
By simplifying, we get –
$\Rightarrow \dfrac{23}{2}=25$ .
Again it is not true.
So, $w=5$ is also not the solution.
Now, we let $w=7$ .
We put $w=7$ in $\dfrac{3w+8}{2}=25$. We get –
$\Rightarrow \dfrac{3\times 7+8}{2}=25$ .
By simplifying, we get –
$\Rightarrow \dfrac{29}{2}=25$ .
This is not true.
So, $w=7$ is also not a solution.
As we can see that the distance on the left side and right side is decreasing means we are in the right direction.
So, now let $w=10$ .
So, putting $w=10$ , we get –
$\begin{aligned} & \Rightarrow \dfrac{3\times 10+8}{2}=25 \\\ & \Rightarrow \dfrac{38}{2}=25 \\\ \end{aligned}$
By, simplifying, we get –
$\Rightarrow 19=25$ again not true.
Hence not the solution to our problem.
Now we let $w=14$ .
We put $w=14$ in $\dfrac{3w+8}{2}=25$ , we get –
$\Rightarrow \dfrac{3\times 14+8}{2}=25$
By simplifying, we get –
$\begin{aligned} & \Rightarrow \dfrac{50}{2}=25 \\\ & \Rightarrow 25=25 \\\ \end{aligned}$ .
Which is true, so $w=14$ is the solution of $\dfrac{3w+8}{2}=25$ .

Note: Another way to solve this is to use the arithmetic tool.
Now, as $\dfrac{3w+8}{2}=25$
We multiply both sides by 2, we will get –
$\Rightarrow \left( \dfrac{3w+8}{2} \right)\times 2=25\times 2$
By simplifying, we get –
$\Rightarrow 3w+8=50$
Now subtract 8 from both sides, we get –
$\Rightarrow 3w+8-8=50-8$
By simplifying, we get –
$\Rightarrow 3w=42$
Divide both sides by 3, we get –
$\Rightarrow \dfrac{3w}{3}=\dfrac{42}{3}$ .
So, $w=14$ , Hence the solution of $\dfrac{3w+8}{2}=25$is $w=14$ .