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7th Grade Math / Lesson 4: Solving Equations II

SOLVING EQUATIONS
What will we be learning in this lesson?


  • In this lesson, you will learn how to use inverse operations to solve an equation.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


Solving Equations


  • This section is similar to the last section. The difference is that this section deals with the inverse operations of multiplication and division. In the last section, it was all adding and subtracting.


Solving Equations


  • An inverse operation is something that does the opposite of the original action.

  • Inverse operation can be used to find a solution to an equation.

  • If the variable can be isolated (by itself), the solution can be found.

    4x = 32

  • Here the variable has a "times 4" with it. To undo the "times 4", you need to find the inverse operation.

  • The inverse operation of "times 4" would be "divide by 4".

  • Using this inverse operation, we can find the solution to this equation.


Solving Equations


  • Look at this series of events.

  • What do you get at the end of the series?


Solving Equations


  • Look at this series of events.



  • What do you get at the end of the series?

  • Since multiplying by 4 and dividing by 4 are opposites of each other, they undo any action that was made.

  • Like putting on socks then shoes, and then taking off shoes and socks takes you right back to having bare feet.

  • It is the same concept with inverse operations in math. They undo each other and take you back to what you started with.

    So, at the end of the series, you have x. Just what you started with.


Solving Equations


  • How will this help when solving an equation? Like this :

    5x = 35

  • To solve this, we need to get x by itself. This means that we need to undo the "times 5" part of the problem.

  • What is the opposite of times 5"?

  • The opposite of "times 5" is "divide by 5" so this is the action that we use to solve this equation for x.

    5x 5 = 35 5

  • Notice that the divide by 5 will undo the multiply by 5 part and leave you with just x.

  • This leaves just the 35 5 to figure out to get the solution. 35 5 = 7 so,

    The solution to the equation is x = 7.


 
Solving Equations


  • Try another one :

    X 2 = 14

  • To solve this, we need to get x by itself. This means that we need to undo the divided by 2 part of the problem.

  • What is the opposite of divided by 2?

  • The opposite of divided by 2 is multiply by 2 so this is the action that we use to solve this equation for x.

    x 2 * 2 = 14 * 2

  • Notice that the times 2 will undo the divided by 2 part and leave you with just x.

  • This leaves just the 14 * 2 to figure out to get the solution. 14 * 2 = 28 so,

    The solution to the equation is x = 28.


 
Solving Equations


  • Any solution that you find by using the inverse operation method can be checked to see if it is the correct solution

    For the equation 5x = 35 we discovered that the solution was x = 7.

  • To check this solution, just put the 7 into the equation for x and make sure that it works.

    5x = 35  Original equation

    5 * 7 = 35 ?  Plug the number in

    35 = 35   See if it works

    Yes, the result is 35 when you plug the solution into the problem. This means that the solution of x = 7 is correct.


  • Can you find and use the correct inverse operation to solve an equation?

  • Can you put a solution into the equation to make sure that it works?

  • Go back to the classroom to get to your homework and any other items you need to attend to.