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Solving for varibles

Q:  Here are three questions in one that involve solving for variables:

(a)  -2x = 5x + 18

(b)  4e + 3 = 7e + 9

(c)  c – 1 = -11 + 3c

A:  OK.  Whenever you are solving for a variable, you want to get all the x’s on one side, and all the plain numbers on the other side:

(a)  -2x = 5x + 18

Subtract 5x from both sides (that will get rid of the x’s on the right side of the equation and put them on the left side:

-2x – 5x = 5x + 18 – 5x

Simplify:

-7x = 18

Now, divide both sides by -7 to really get the x by itself!

-7x/-7 = 18/-7

x = 18/-7

And, there you go!

(b)  4e + 3 = 7e + 9

I will subtract 4e from both sides (putting all of the e’s on the right side):

4e + 3 – 4e = 7e + 9 -4e

Simplify

3 = 3e + 9

Now, subtract 9 from both sides:

3 – 9 = 3e + 9 – 9

-6 = 3e

Divide both sides by 3:

-6/3 = 3e/3

-2 = e

TADA!  See that each one of my steps always makes progress in getting the variable by itself?

(c)  c – 1 = -11 + 3c

Subtract c from both sides:

c – 1 – c = -11 + 3c – c

-1 = -11 + 2c

Add 11 to both sides:

-1 + 11 = -11 + 2c + 11

10 = 2c

Divide both sides by 2:

10/2 = 2c/2

5 = c

One thought on “Solving for varibles

  1. Okk thanks soo much im still having a little trouble with this stuff!! But im getting better thanks to you!!<33

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