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how to solve equation or formula for the variable specified. State what property allows you to take each step.

1. 7c = x, for c


2. q - r = r, for r


3. 7a - b = 15a, for a


4. x - 2y = 1, for y


5. 7f + y = 5, for f


6. rx - 2n = y, for x


7. kn = 4f = 9v, for n


8. x-c/2 = d, for x


9. p+9/5= n, for p


10.3/5m + a = b, for m


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2 Answers

1. Multiplicative Inverse




2. q*r - r=0: Additive Inverse (Subtraction)

r*(q-1)=0: Distributive Property

r=0/(q-1) or r=0, Multiplicative Inverse


7a - 15a -b=0: Additive Inverse (Subtraction)

-8a -b=0

-8a -b +b=0+b: -b +b, which are inverses of each other, form 0, the identity of Addition

In order to solve these equations, you'll have to understand the opposite properties of order of operations.

  1. Addition is the opposite of Subtraction
  2. Multiplication is the opposite of Division

Another thing with these problems.  When solving for a variable, you're going to want to move every term that has the variable in it to one side of the equals sign.

With these, we can do a couple of these as examples.

2.  Q - R = R  : Solve for R

    • You have an R by itself on the right side of the equals sign, so move the R on the left side to the right side, by doing the opposite (adding in this case) to both sides (Q - R + R = R + R)
    • Simplify this (Q = 2R)
    • Now you have 2R (2 multiplied by R) on the right side, and you're solving for R, so you'll have to do the opposite (dividing in this case) to both sides (Q/2 = 2R/2)
    • Simplify this (Q/2 = R)
    • You're done!

5.  7F + Y = 5 : Solve for F

    • The variable you're solving for (F) is on the left side of the equation, therefore we'll be moving everything else to the right side.
    • First step, move what isn't attached to the variable (Y) by doing the opposite of addition to both sides (7F + Y - Y = 5 - Y)
    • Simplify (7F = 5 - Y)
    • Now all we need to do is move the 7 (divide in this case) (7F/7 = (5 - Y)/7 )
    • Simplify (F = (5 - Y)/7 )
    • Done!

If you have any more questions, let me know!