​Solving Equations

​To solve for a variable means to isolate the variable on one side of the equation.

• ​Isolate means to get it by itself

• A variable is a letter that represents an unknown quantity.

​How do you isolate the variable?

​We isolate variables by using inverse (opposite) operations. We do the same operations to both sides of the equation to get everything to the other side of the equation from the variable.

• For example, with 2x = 8, you would move the two to the other side by dividing both sides by 2, leaving x = 4

​Two-Step Equations

​2x = 8 is a one-step equation because only one thing is being done to the x (times 2), so we only have to do one thing to solve it (divide by 2).

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In two-step equations, there are TWO things being done to the variable, so we have to take two steps to solve it.

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​For example, in the equation 2x + 5 = 9, we have to get both "plus 5" and "times 2" off of the left side in order to isolate x.

​Which Step First?

​How do you know which step to take first when there is more than one step?

​Work backward.

​In the equation 2x + 5 = 9, notice that what's happening:

• ​x is being multiplied by 2

• ​Then 5 is added to it

​So to undo those steps, work backward until you get back to the x:

• ​Subtract 5 from both sides

• ​Divide both sides by 2

​OK, ready to solve some 2-step equations?

​Get your scratch paper ready.

​On your marks.

​Get set...

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​

​

​go

​And now, something different

​Take a look at this problem to the right. It kind of looks like a one-step equation, but it's actually a two-step equation in disguise.

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​What do you think the two solving steps should be? The next slide is the question.

Level up!

​Take a look at THIS problem to the right. It might look harder, but if you follow the earlier advice (work backward), it makes perfect sense.

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​Just think: what is happening to the m, then reverse it.

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​The question is the next slide.