Question

How do you solve $a+5=-5a+5$?

Answer 1

Hint: In this question we need to solve a given equation in terms of a and find the value of ‘a’ which satisfies the equation. For this we will start applying the operations on both sides of the equation such that the equation is reduced in a way that there is the variable s left on the left side of the equation and a constant term on the right side of the equation. The constant term found will be the required value of a satisfying equation. The operations that can be used are addition, subtraction, multiplication and division.

Complete step by step answer:
Here we are given the equation in terms of a as $a+5=-5a+5$. We need to solve it to find the value of ‘a’ such that it satisfies the equation. For this, let us try to convert the equation into the form a = c where c is constant using the operation addition, subtraction, multiplication and division.
The equation is $a+5=-5a+5$.
As we can see, we have the constant 5 extra on the left side of the equation so, let us remove it. For removing 5 let us subtract 5 from both sides of the equation we get $a+5-5=-5a+5-5$.
Subtracting 5 from 5 gives us 0 so the equation reduces to $a=-5a$.
Now I want a variable only on the left side of the equation. So let us remove 5a from the right side of the equation. For this, let us add 5a on both sides of the equation we get $a+5a=-5a+5a$.
Simplifying and adding the like terms we get $6a=0$.
As we can see the equation is still not in the form a = c as there is a coefficient of ‘a’ which we need to remove. For this let us divide by 6 on both sides of the equation we get $\dfrac{6a}{6}=\dfrac{0}{6}$.
We know that 6 divided by 6 gives us 1 and 0 divided by any number gives us 0. So the equation becomes a = 0.

Therefore the required value of ‘a’ is 0.

Note: Students should take care of the signs while solving the equation. Use proper notation where required. Students can also check their answers by following way,
To check let us put the value of a = 0 in the original equation $a+5=-5a+5$ we get $0+5=-5\left( 0 \right)+5$.
Simplifying we get $5=0+5\Rightarrow 5=5$.
Left side of the equation is equal to the right side. Hence value of a as 0 satisfies the equation.