An equation with addition subtraction multiplication distributive property and a variable on both sides

Question

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Answer 1

Sarah M. gave a cool answer (be sure to read it).

 

Now, I'll tell you how to get an equation like the one Sarah M. started with:

 

The desired result is:

  "An equation with addition subtraction multiplication distributive property and a variable on both sides"

 

So, we know there will be an equation and a solution for some variable; let's pick a solution for our variable:

    x = 5

 

To get a variable on both sides, it is easier to do that first:

   x + x = x + 5

    2x = x + 5

Cool ! That also takes care of multiplication and addition.

 

Then, distributive property, because we don't want to subtract when we have just added.

   3(2x+4) = 3(x+9)

   3(2x+4) = 3x + 27             (to make the right side look different)

 

Subtract 7:

  3(2x+4) - 7 = 3x + 20

 

Now, you have learned how teachers make up problems that have an easy answer.

 

Oh, by the way, you should solve the equation,  3(2x+4) - 7 = 3x + 20, so your students won't complain that you gave them a bad problem.

Answer 2

How about this one?

5(-4y + 3) = 2(1 - 8y) + 11

 -20y + 15 =   2 - 16y + 11      Step 1: Distribute (This is the M in PEMDAS)

 -20y + 15 = 13 - 16y              Step 2: Combine Like Terms (2+11=13)

+16y                 +16y              Step 3: move all the variable terms (terms with a letter) to one side of the equation

   -4y +15 = 13 + 0

   -4y +15 = 13

         -15    -15                       Step 4: move all the constants (numbers without a letter) to the other side of the equation

   -4y + 0  =  -2

          -4y = -2

      -4y/-4 = -2/-4                   Step 5: Divide both sides by -4

              y=1/2

 

Here's a cheer to remember (steps 3 and 4) for equations with variables on both sides (Bonus points for doing the choreography too):

 

Letters to the Left           (Swing your arms to the left)

Numbers to the Right      (Swing your arms to the right)

Stand-Up Sit-Down         (Actually stand up and sit down)

Fight Fight Fight             (Fist pumping in the air)

 

This will help you to remember that all the variable terms need to be on one side of the equation together and all the constants need to be on the opposite side together as part of the goal for your inverse operations.