Solving Two-Step Equations                  Page 2 of 4

Solving Two-Step Equations

Let's say I have a mystery number.  If I multiply it by 2 and then add 5, I get 11.  Can you figure out what the number is?  Let's write this situation as an equation using the variable x.  If I multiply it by 2, I can represent that as 2x.  To show that I add 5 next, I can write 2x + 5.  This comes out to 11 so my equation is:

​How do you solve for x?  You need to work your way backwards to get x by itself.

The last step was to add 5, so we need to undo that first.  How do we undo adding 5? We need to use the inverse operation and subtract 5 from both sides.  When solving a two-step equation, you will always need to undo the addition and subtraction first.

Why do you undo addition and subtraction first?  Let's say you knew what x was.  If you plugged it in, you would have to follow the order of operations to simplify.  A lot of teachers use PEMDAS, or Please Excuse My Dear Aunt Sally to remember the order.  If you follow the order of operations, you need to multiply and divide before you add or subtract.  

When you're simplifying, the addition and subtraction are always done last.  When you're solving, you're working your way backwards to solve for x.  This means you'll need to undo the addition and subtraction first.  ​

​To solve the equation 2x + 5 = 11 we subtracted 5 from both sides first.  Now that we've canceled out the addition, we're left with the equation 2x = 6.  The 2 in front of the x means that x is being multiplied by 2.  To get x by itself, we need to undo this multiplication.  How do you undo multiplying? You need to divide.  We can can cancel out the 2 by dividing both sides by 2.  Remember to always do the same thing to BOTH sides to make sure the equation stays balanced.

How do you check your answer?  Plug 3 in for x in the original equation and make sure the left side simplifies to 11.  2(3) + 5 = 6 + 5 = 11. It works!   Go to the next page to see a second example.

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