Question

How do you solve 3x-5=7x+3?

Answer 1

Hint: This type of problem is based on the concept of linear equations with one variable. Here, we first consider the given equation. Then, subtract the whole equation by 3x and simplify. And bring all the x terms to the LHS and the constants to the RHS. We get an equation with variable x. divide the whole equation by 5 and do necessary calculations to find the value of x which is the required answer.

Complete step by step answer:
According to the question, we are asked to solve 3x-5=7x+3.
We have been given the equation is 3x-5=7x+3. ---------(1)
We first have to consider the equation (1).
Subtract the whole equation by 3x. We get,
3x-3x-5=7x+3-3x
We know that terms with the same magnitude and opposite signs cancel out. Here, cancelling 3x, we get
-5=7x-3x+3
\[\Rightarrow 7x+3-3x=-5\]
Let us now group all the x terms and simplify.
\[\Rightarrow \left( 7-3 \right)x+3=-5\]
On further simplification, we get
4x+3=-5
Now, subtract 3 from both the sides of the equation.
\[\Rightarrow 4x+3-3=-5-3\]
We know that terms with the same magnitude and opposite signs cancel out. Here, cancelling 3, we get
4x=-5-3
On further simplification, we get
4x=-8
Now, divide the whole obtained equation by 4.
\[\Rightarrow \dfrac{4x}{4}=\dfrac{-8}{4}\]
We can express the equation as
\[\dfrac{4x}{4}=\dfrac{-4\times 2}{4}\]
We find that 4 are common in both the numerator and denominator of both the LHS and RHS.
Let us cancel the common terms.
We get x=-2.

Therefore, the value of x in the equation 3x-5=7x+3 is -2.

Note: We can verify whether the answer obtained is correct or not.
Substitute the value of x in the given equation and check whether the LHS is equal to RHS.
Consider equation (1), that is 3x-5=7x+3.
Here, LHS=3x-5
But we know that x=-2.
Therefore, we get
LHS=3(-2)-5.
On further simplifications, we get
LHS=-6-5
Therefore, LHS=-11.
Now consider the RHS.
RHS=7x+3
But we know that x=-2.
On substituting the value of x in RHS, we get
RHS=7(-2)+3
On further simplification, we get
RHS=-14+3
Therefore, RHS=-11
Here, LHS=RHS.
Hence the obtained answer is correct.