Question

How do you solve $ 6r+7=13+7r $?

Answer 1

Hint: In this question, we need to solve the given equation which means we need to find the value of r which satisfies this equation. For this, we will use a stepping method i.e. we will try to add/subtract/multiply/divide some terms into both sides of the equation such that we are left with only variables on the left side and a constant term on the right-hand side. That value of constant will be the required value of r which satisfies the equation.

Complete step by step answer:
Here we are given the equation as $ 6r+7=13+7r $.
We need to find the value of r which will satisfy the given equation. For this, we need to modify the equation in the form as r = c where c will be a constant.
As we can see, we want only variable r on the left side of the equation. So, let us remove the constant term 7 from the left-hand side.
Subtracting 7 from both sides of the equation we get $ 6r+7-7=13+7r-7 $.
Simplifying the like terms on both sides we get $ 6r=7r+6 $.
(Here we have subtracted 7 from 13 to 6).
Now we want only constant term on the right side of the equation. So we need to remove 7r from the right side of the equation.
Subtracting 7r from both sides of the equation we get $ 6r-7r=7r+6-7r $.
Subtracting like terms on both sides we get $ -r=6 $ .
As we can see, the variable is negative but we cannot have a negative variable. A constant can be negative therefore, taking negative on both sides we get $ -\left( -r \right)=-6\Rightarrow r=-6 $ .
We can see the equation has been converted to the form r = c so, the value of r is equal to -6.
Hence -6 is the required answer.

Note:
Students should carefully perform all the operations by adding/subtracting every term on both the sides of the equation. They can also check their answer by following way,
Putting r = -6 in the original equation we have,
  $ 6\left( -6 \right)+7=13+7\left( -6 \right)\Rightarrow -36+7=13-42\Rightarrow -29=-29 $ .
As we can see, the left-hand side is equal to the right-hand side. Therefore, the value of r as -6 satisfies the equation.