Solving two-step equations when the variable is on both sides: Solving two step equation when the variable was on one side of the equation contains unknown only on the left or right side of the equation. To understand this topic better you need to know how to solve one-step equations. Here the unknown is on both sides of the equation. Consider an equation,
50 – 10x = 40x
In such cases takes the unknown on one side of the equation. You can bring all unknowns on the left side or right side of the equation.
The best way is to have them together on the side that has fewer operations. In this case, the left-hand side of the equation has subtraction involved while the right side of the equation has nothing. So it’s good to have unknowns on the right side.
Also, our rule says whatever operation you perform on one side of the equation, the same has to be performed on the other side of the equation.
50 – 10x + 10x = 40x + 10x
50 = 50x
Since the right side of the equation contains the variable term, we must first divide 50 on each side of the equation
Dividing both sides by 50 gives,
50/50 = 50x/50x
1 = x
So, x = 1
What happens when I bring the unknowns to the left side of the equation while solving two step equations?
50 – 10x = 40x
Subtracting 40x from both sides
50 – 10x -40x = 40x – 40x
50 – 50x = 0
Subtracting 50 from both sides,
50 – 50 – 50x = 0 – 50
– 50x = -50
Dividing by -50 on both sides
-50x/-50 = -50/-50
x = 1
The value of x still comes out to be the same, but the steps followed in the first approach are less than the second.
To solve any equation:
- Bring unknowns on one side of the equation
- Perform inverse operations on it.
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