Basics of solving equations with variables
Topic Notes
In this lesson, we will learn:
- How to isolate the variable in an equation by using equation models, or by doing the operation to both sides to rearrange equations
- How to understand multiplication and division questions using the phrase “times as many” with the “times as many’ model
Notes:
- A systematic way to solve equations and find unknown variables is to isolate the variable:
- We want the unknown variable by itself on one side of the equal sign (=) and only numbers on the other side so that the operation can be completed
![Introduction to Solving Equations with Variables](https://dmn92m25mtw4z.cloudfront.net/img_set/math4-6-3-x-1/v1/math4-6-3-x-1-473w.jpg)
- Recall the equation models for the four operations. Equation models can help rearranging parts of an equation to isolate the variable. Any simple equation can be rewritten in 3 ways. Out of the three ways, one version will have the unknown variable by itself.
![Introduction to Solving Equations with Variables](https://dmn92m25mtw4z.cloudfront.net/img_set/math4-6-3-x-2/v1/math4-6-3-x-2-718w.jpg)
- When equation parts are side by side, you will be adding/multiplying; when equation parts are on top of each other, you will be subtracting/dividing
![Introduction to Solving Equations with Variables](https://dmn92m25mtw4z.cloudfront.net/img_set/math4-6-3-x-3/v1/math4-6-3-x-3-986w.jpg)
- You can also isolate the variable by “doing the opposite
operation to both sides”: - Word problems using the phrase “times as many” may need multiplication or division:
- Use the “times as many” model to decide which operation to use
![Introduction to Solving Equations with Variables](https://dmn92m25mtw4z.cloudfront.net/img_set/math4-6-3-x-5/v1/math4-6-3-x-5-986w.jpg)