Question

How do you solve $4x-1=-9$?

Answer 1

Hint: In this question we have to solve the given linear equation that is, \[4x-1=-9\]. It means that we have to find the possible value of \[x\] for which the given equation is satisfied (It means that on substituting that particular value of \[x\] in the equation it will turn out to be zero). So, for that we will try to remove the constant term from the given equation, and after that we will try to make the coefficient of \[x\] as \[1\]. While during this we have to make sure that we have to keep the equation balanced throughout the procedure.

Complete step-by-step solution:
In the question we have given linear equation with one variable is,
\[\Rightarrow 4x-1=-9........(i)\]
In order to solve the given linear equation we will \[a\] add \[1\] on both sides to isolate \[x\].
\[\Rightarrow 4x-1+1=-9+1\]
\[\Rightarrow 4x=-8\]
Now , on dividing by \[4\] on both sides we get,
\[\Rightarrow \dfrac{4x}{4}=-\dfrac{8}{4}\]

Which further implies as \[x=-2\] is the required answer.

Note:
First we will understand what the solution is.
“A value, such that, when you replace the variable with it, makes the equation true”.
That is, the left hand side comes out equal to the right hand side.
Let us consider a linear equation of the form \[ax+b=c\] ; where \[a,b\] and \[c\] are constant.
Solving a linear equation is to get the variable you are solving for alone on one side and everything else on the other side using inverse operations.
There are some tools that we need to solve the linear equations.
(1) Addition and subtraction properties of equality that is
If \[a=b\] then
\[\Rightarrow a+c=b+c\]
And if \[a=b\] then
\[\Rightarrow a-c=b-c\]
In other words, if two expressions are equal to each other and if we add or subtract the exact same thing to both sides, then two sides will remain equal.
(2) Multiplication and division properties of equality.
That is,
If \[a=b\] then
\[\Rightarrow a\times c=b\times c\]
And if \[a=b\] then
\[\Rightarrow \dfrac{a}{c}=\dfrac{b}{c}\] ; Where \[c\] is not equal to zero.
In other words, if two expressions are equal to each other and if we multiply or divide (except for zero) the exact same constant to both sides then the two sides will remain equal. In short we can say that do onto one side of the equation, what you do to the other side of the equation.
In short we can say that
Do onto one side of the equation, what you do to the other side of the equation.
In simple words, we can say that,
If you add, subtract, multiply or divide or one side of the equation. You have to do the same thing on the other side of the equation as well. i.e. we must always keep the equation balanced so that both sides are equal.
So, we can conclude the steps for solving linear equation as follows:
(1) Simplify each side. If needed.
This would involve things like removing (), — (bar), fractions etc.
(2) Use the add and subtract properties to move the variable to one side and all other terms to the other side.
(3) Use the multiplication and division properties to remove any values that are in front of the variable.
(4) Check your answer.