Question

How do you solve $\dfrac{2}{3}x-7=-3$ ?

Answer 1

Hint: We are given an equation as $\dfrac{2}{3}x-7=-3$ , we are asked to solve, mean we will look for that value of ‘x’ which will satisfies the given equation, to do so we will use hit and trial method , in this method we will assume the value of ‘x’ and check whether it satisfies the equation or not, the value which satisfies the equation will become solution. We can also use algebraic tools to solve our problem, tools like $+,\times ,\div ,-$ etc.

Complete step by step answer:
We are given $\dfrac{2}{3}x-7=-3$, it is a linear equation as it has degree (highest power) as 1 so it can have just one solution.
To find the solution (those values which satisfy the equation) we will work on the various values and check which one will satisfy the equation.
Now, as we have $\dfrac{2}{3}x-7=-3$.
We let $x=3$ .
Then putting $x=3$ in $\dfrac{2}{3}x-7=-3$, we get –
$\Rightarrow \dfrac{2}{3}\times 3-7=-3$
By simplifying, we get –
$\begin{align}
  & \Rightarrow 2-7=-3 \\
 & -5=-3 \\
\end{align}$
Which is not true.
So, $x=3$ is not the solution.
Now, let $x=6$ .
We put $x=6$ in $\dfrac{2}{3}x-7=-3$, we get –
$\Rightarrow \dfrac{2}{3}\times 6-7=-3$
By, simplifying, we get –
$\begin{align}
  & \Rightarrow 2\times 2-7=-3 \\
 & \Rightarrow 4-7=-3 \\
\end{align}$
So, we get –
$\Rightarrow -3=-3$ .
Which is true.
So, $x=6$ is the solution of our equation $\dfrac{2}{3}x-7=-3$.

Note:
The flow in that method is just that if we start our solution using a value of ‘x’ and we move down a wrong path then it will take a lot of time to get the correct solution. So we can use another way, which solves the problem using algebraic in such addition, division, multiplication and more.
Now as our equation is $\dfrac{2}{3}x-7=-3$ .
We will add ‘7’ on both sides, we get –
$\Rightarrow \dfrac{2}{3}x-7+7=-3+7$
By simplifying, we get –
$\dfrac{2}{3}x=+4$ (as $-7+7=0$ and $-3+7=4$ )
Now, we will multiply both sides by 3.
So, $\Rightarrow \dfrac{2}{3}x\times 3=4\times 3$
By, solving, we get –
$\Rightarrow 2x=12$
Now to separate ‘2’ from ‘x’, we divide both sides by ‘2’, so, we get –
$\Rightarrow \dfrac{2x}{2}=\dfrac{12}{2}$
By solving, we will get –
$x=6$
So, $x=6$ is the required solution.
Also remember that we can never add unlike terms. That is we cannot add a constant with a term with a variable like if we do $x+2=2x$ or $2x+4=6x$ then their calculations are incorrect. We can multiply unlike terms but cannot add or subtract.