Answer:
m = -4
Step-by-step explanation:
You want the solution to the "two step" equation m -4 = 2m.
Two-step equation
A "two-step" linear equation is one that can be solved in two steps. The steps in general are ...
- addition of something
- multiplication by something
The "inverse" properties of addition and multiplication are used to identify the quantities added or multiplied.
Forms of a two-step equation
There are two forms a two-step equation might take:
ax +b = c
ax +b = cx
You will notice that one side of the equal sign has a sum of two terms: a term with the variable, and a constant term without the variable. The other side of the equation will have one term, which may be either a constant term or a variable term.
First step
The idea of the first step is to make sure the variable term ends up on one side of the equal sign, and the constant term ends up on the other side.
The parts of the first step are ...
- identify the kind of term on the side of the equation with one term
- identify the term of the same kind on the other side of the equal sign
- add the opposite of that identified term to both sides of the equation.
For the given equation ...
m - 4 = 2m
The term by itself is a variable term. The variable term on the other side of the equation is "m". The first step will be to add "-m" to both sides of the equation.
m -4 -m = 2m -m . . . . . . -m added to both sides
-4 = m . . . . . . . . . . . . . simplify
Now, we have a variable term (m) on one side of the equal sign, and a constant term (-4) on the other side. This is the desired result of the first step.
Second step
The idea of the second step is to make the coefficient of the variable be 1. We do that by multiplying both sides of the equation by the reciprocal (inverse) of the coefficient of the variable.
For the equation ...
ax = b
we multiply by the reciprocal of 'a', which is 1/a.
(ax)(1/a) = b(1/a)
x = b/a . . . . . . . . . . . effectively, we're dividing by 'a'
In the given equation, we have ...
-4 = m
which already has a coefficient of 1 on the variable m. This means we're done, and no additional step is actually needed.
The solution is m = -4.
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Additional comment
There is another form of 2-step equation you may see occasionally:
a(x +b) = c
Solving this can be done by reversing the order of the steps: first divide by the coefficient of x, then subtract the constant.
x +b = c/a
x = (c/a) -b
If the variable term inside parentheses has a coefficient other than 1, it may be useful to eliminate parentheses using the distributive property, then solve like a regular 2-step equation.
