Question
Question: How do you solve \(6x-3=8x-9\)?...
How do you solve 6x−3=8x−9?
Solution
The equation given in the above question, which is written as 6x−3=8x−9, is a linear equation in a single variable, which is x. Therefore, it will have a unique solution. Now, for solving the given equation we need to separate the variable terms on the LHS and the constant terms on the RHS. For this, we need to add 3 on both sides of the given equation to get 6x=8x−6. Then we have to subtract 8x from both sides to get −2x=−6. Finally, on dividing both the sides by −2, we will get the final solution of the given equation.
Complete step by step solution:
The equation given in the above question is
⇒6x−3=8x−9
We can see that the highest power of the only variable x in the above equation is equal to one. Therefore, we can say that the given equation is a linear equation in a single variable. This means that it will have a unique solution.
Adding 3on both the sides of the above equation we get
⇒6x−3+3=8x−9+3⇒6x=8x−6
Now, we add 8x on both the sides of the above equation to get
⇒6x−8x=8x−6−8x⇒−2x=−6
Multiplying −1 both the sides, we get