Solve 2-Step Equations

Solve 2-Step Equations

by Robert Potter

​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.

Multiple Choice

Which of the following equations is solved for x?

• $$2x=12$$  

• $$x=2,000$$  

• $$x\ +\ 7=20$$  

• $$\frac{x}{5}=10$$  

Multiple Choice

Which of the following equations is solved for x?

• $$x+x=10$$  

• $$x+y=1$$  

• $$x\ +\ 7=20$$  

• $$x=\frac{9}{32}$$  

​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

Multiple Choice

Which of the following shows the correct inverses of each operation?

• add--> subtract

  subtract--> multiply

  multiply--> divide

  divide--> add

• add--> subtract

  cook--> freeze

  subtract--> multiply

  eat--> throw up

• add--> subtract

  multiply--> subtract

  divide--> add

  subtract--> add

• add--> subtract

  multiply--> divide

  subtract--> add

  divide--> multiply

​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).

​

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

​

​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

Multiple Choice

What is the first step you should take to solve this equation: 10x + 10 = 20

• Subtract 20 from both sides

• Divide both sides by 10

• Multiply both sides by 10

• Subtract 10 from both sides

Multiple Choice

What are the two steps you should take to solve this equation: $$\frac{x}{10}-10=20$$  

• Multiply both sides by 10, then subtract both sides by 10

• Divide both sides by 10, then add 10 to both sides

• Add 10 to both sides, then multiply both sides by 10

• Subtract 10 from both sides, then multiply both sides by 10

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

​Get your scratch paper ready.

​On your marks.

​Get set...

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​

​go

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​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.

​

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

Multiple Choice

What are the solving steps to isolate q?

• Subtract 61 from both sides, then add 1 to both sides

• Subtract 61 from both sides, then divide both sides by -1

• Add 61 to both sides, then divide by -q

• Add 61 to both sides, then divide by -1

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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.

​

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

​

​The question is the next slide.

Multiple Choice

What are the solving steps to isolate m?

• Multiply both sides by 31, then subtract 112 from both sides

• Subtract 31 from both sides, then subtract 112 from both sides

• Subtract 112 from both sides, then multiply both sides by 31

• Divide both sides by 31, then subtract 112 from both sides

Multiple Choice

What are the solving steps to isolate d?

• Multiply both sides by 6, then subtract 61 from both sides

• Subtract 6 from both sides, then subtract 61 from both sides

• Subtract 61 from both sides, then multiply both sides by 6

• Divide both sides by 6, then subtract 61 from both sides