Question

How do you solve $43x-43=-42x-42$ ?

Answer 1

Hint: We are asked to find the solution of $43x-43=-42x-42$
Firstly, we learn what the solutions of the equation mean, then we will learn what linear equation is in one variable term. We use a hit and trial method to find the value of ‘x’. In this method we put the value of ‘x’ one by one by hitting arbitrary values and looking for needed values. Once we work with a hit and trial method we will try another method where we apply algebra. We subtract, add or Multiply terms to get to our final term and get our required solution. We will also learn that doing the questions using algebraic tools makes them easy.

Complete step by step answer:
We are given that we have $43x-43=-42x-42$ We are asked to find the value of ‘x’, or we are asked how we will be able to solve this expression.
Solution of any problem is that value which when put into the given problem then equation is satisfied
Now we learn about the equation on one variable. One variable simply represents the equation that has one variable $\left( \text{say x, y or z} \right)$ and another one constant.
For Example:
$x+2=4,2-x=2,2x,2y$ etc.
Our equation $43x-43=-42x-42$ also has just one variable ‘x’.
We have to find the value of ‘x’ which will satisfy our given equation.
Firstly we try by the method of hit and trial. In which we will put a different value of ‘x’ and take which one fits the solution correctly.
Let $x=0$
Putting $x=0$ in $43x-43=-42x-42$ we get –
$43\times 0-43=-42\times 0-42$
So, $-43=-42$
Not true.
So, $x=0$ is not a solution.
Let $x=1$
We put $x=1$ in $43x-43=-42x-42$ we get –
$\begin{align}
  & 43\times 1-43=-42\times 1-42 \\
 & 0=-42-42 \\
 & 0=-82 \\
\end{align}$
Not true.
So $x=1$ is not a solution.
Let $x=1$
We put $x=-1$ in $43x-43=-42x-42$ we get –
$43\left( -1 \right)-43=-42\left( -1 \right)-42$
So we have –
$\begin{align}
  & -43-43=+42-42 \\
 & -86=0 \\
\end{align}$
Not true hence $x=-1$ is also not true.
We can see that hit and trial method here for equation having big number like 43 42 and other is difficult to find to do it in a simple way we will use another way in which we will use algebraic tools like adding subtracting division and Multiplication of the terms to simplify and solve the given problem
Now
We are given with
$43x-43=-42x-42$
We will separate the variable on one side and constant on other
So we add 42x on both side and add 43 on both side so –
We get –
$43x-43+42x+43=-42x-42+43+42x$
Cancelling like terms we get –
$85x=1$
Now we divide both sides by 85
So on the right we get $\dfrac{1}{85}$ and on the left we get ‘x’.
So $x=\dfrac{1}{85}$
Hence the solution is $\dfrac{1}{85}$

Note:
Remember that, we cannot add the variable to the constant. Usual mistakes like this where one adds constants with variables usually happen.
For example: $3x+6=9x$ here one added ‘6’ with 3 of x made it 9x, this is wrong, we cannot add constant and variable at once. Only the same variables are added to each other.
When we add the variable the only constant part is added or subtracted.
That is $2x+2x=4x$ error like doing it $2x+2x=4{{x}^{2}}$ may happen so be careful there
Remember when we divide positive terms by negative values the solution we get is a negative term this may happen that we skip – sign.