Concept explainers
Compare and contrast solving equations with variables on both sides of the equation to solving one − step or multi-step equations with a variable on one side of the equation.
Answer to Problem 47HP
One − step equation is simple but multi − step equation has more steps while solving both separately.
Explanation of Solution
Given:
Concept Used:
We need to compare how to solve the multi − step equation with one − step equation with variables on both sides.
1
| When solving an equation with variables on both sides, we must ass or subtract to get all the terms with the variable on one side, add or subtract to get the terms that are constant on the other sides, and then multiply or divide to solve for the variable. In the example to the left, the steps are :
(1) Example equation. (2) Subtract 3x on both sides. (3) Add 2 on both sides. (4) Divide both sides by 2. |
2
| When solving a one − step equation, you only need to do one operation of adding, subtracting, multiplying or dividing to solve for the variable. When solving a multi − step equation, you need to add or subtract to get all the terms with no variables to the other side and then multiply or divide to solve for the variable.
The steps for the example to the left are: (1) Example equation. (2) Add 2 on both sides (3) Divide both sides by 2 |
Conclusion:
The difference between solving an equation with variables on both sides compared to one − step or multi − step equations is that you have the additional steps of getting all the variable terms on one side. Once that is done, the equation becomes a multi − step or one − step equation so the remaining steps are the same. Note that in the examples above; once 3x was subtracted on both sides of the first example, it becomes a multi − step equation and once 2 was added on both sides of both examples, it becomes one − step equation.
Thus, both are having same method for solving the equation, the equations with variables on both side is more complex and take more steps for multi − step equation.
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