Question

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

Answer 1

Hint: In this question, we are given an equation in terms of x and we need to find the value of x which satisfies this equation. For this, we will add, subtract, multiply and divide some terms on both sides of the equation such that we have only a variable x on the left side of the equation and a constant on the right side of the equation. The value of the constant will be the required value of x which satisfies the equation.

Complete step-by-step answer:
Here we are given the equation in terms of x as $5x-3=-3x+5$.
We need to find the value of x which satisfies the equation. For this, let us try to make this equation of the form x = c where c is any constant.
The equation is $5x-3=-3x+5$.
As we can see, we have a constant 3 on the left side of the equation which we do not require so let us add 3 on both sides of the equation we get $5x-3+3=-3x+5+3$.
Adding and subtracting constant we get $5x=-3x+8$.
Now as we can see that, there is a term having variable x on the right side of the equation. So let us remove it. For this, let us add the term 3x on both sides of the equation we get $5x+3x=-3x+8+3x$.
Simplifying the like terms we get $8x=8$.
As we can see, x still has a coefficient 8 which we do not require. So let us remove it by dividing both sides of the equation by 8 we get \[\dfrac{8x}{8}=\dfrac{8}{8}\].
As 8 divided by 8 gives 1 so we get x = 1.
It is of the form x = c. Hence the required value of x is 1 which satisfies the given equation.

Note: Students should take care of the signs while adding, subtracting the terms on both sides of the equation. Students can check their answers by putting the value of x as 1 in the original equation and verify left side to be equal to the right side i.e. putting x = 1 in $5x-3=-3x+5$ we get $5-3=-3+5\Rightarrow 2=2$. Left side is equal to the right side. Hence x = 1 is the correct answer.