Solve |2y - 2| = 15

Question

Solve |2y - 2| = 15

Answer 1

You can write this as two equations by saying the positive and negative of the inside of the absolute value is equal to 15.  This will give 2y - 2 = 15 and -(2y-2) = 15.  For the first equation we add two to both sides to get 2y - 2 +2 = 15 + 2.  This givese you 2y = 17.  We then divide both sides by two to get 2y/2 = 17/2 which gives y = 8.5.  Now let's work with -(2y-2) = 15.  We use the distributive property to get rid of the parenthesis and distribute the negative throughout.  We get -2y + 2  = 15.  Subtract 2 from both sides:

-2y +2 - 2 = 15 - 2 = 13.  Now we have -2y = 13.  Now divide both sides by -2 and we get -2y/-2y = 13/-2 which gives y = -6.5.

The last step is to check your answers by plugging in your values you find for y into the original equation.  This gives |2*8.5 - 2| = 15 is true and |2*-6.5 - 2| = 15 is also true.  Your answers are correct!

Answer 2

Solve |2y - 2| = 15

The least confusing way to solve an absolute value problem is to split it into two problems, one for the positive possibility, and one for the negative.  So, we'd split this problem into these two problems:

2y - 2 = 15                 and                       -(2y - 2) = 15

Then, it's just a matter of solving for y:

Multiply both sides of the second equation by -1.

2y - 2 = 15                 and                      2y - 2 = -15

After that, solving the two equations is pretty similar.  First, add 2 to both sides of the equation.  (For BOTH equations.  If solving both equations at once is confusing, feel free not to do it!  You can solve one equation for y, then the other!  I'm just saving a little time.) So, we added 2 to both sides:

2y = 17                        and                     2y = -13

Then, divide both sides by 2:

y = 17/2 = 8.5              and                     y = -13/2 = -6.5

Great!  Now we have y = -6.5, and y = 8.5 .  You can also write this as y = -6.5, 8.5

ANSWER: y = -6.5, 8.5

 

I recommend always checking your answers with absolute value equations.  Let's take those answers and plug them into the original equation.  I'll do y = -6.5 first:

|2(-6.5) - 2| = 15

Order of operations says we multiply first, so:

|-13 - 2| = 15

Now, we subtract 2 from -13:

|-15| = 15

It's not in the standard PEMDAS order of operations, but absolute value brackets come only after everything inside them is as simplified as possible.  The negative inside them becomes a positive:

15 = 15

So y = -6.5 is correct!

Let's try y = 8.5 next:

|2(8.5) - 2| = 15

Same as before, we multiply first:

|17 - 2| = 15

Then, subtract:

|15| = 15

Since the 15 inside the absolute value brackets is already positive, they don't change anything!  We have:

15 = 15

So, y = 8.5 is also correct!

ANSWER: y = -6.5, 8.5

Answer 3

Divide both sides by 2,

|y-1| = 7.5

y-1 = ±7.5

y = 1+7.5 = 8.5

or

y = 1-7.5 = -6.5