Idiot\'s Guides Basic Math and Pre-Algebra

128 Part 2: Into the Unknown

In the equation 7x – 4 = 5x + 2, you might

choose to eliminate 5x. You do that by

subtracting 5x from both sides. Rules about

like terms are important here. You can only

subtract an x-term from another x-term.

You’ll subtract the 5x from the 7x.

Once you’ve subtracted 5x from both sides,

the second variable term is gone, and you

have a two-step equation to solve.

You can eliminate one variable term

by adding or subtracting depending on

the term you want to remove. In the

equation 79 7 19xx, you can eliminate

the variable term on the right side by

subtracting 7x from both sides.

If you prefer, you can eliminate the variable

term on the left side by adding 9x to both

sides.

Either way, you’ll get the same solution.

74 52

55

24 2

xx

xx

x

(^52)
(^25)
521
2
24 2
44
26
2
2
6
2
3
x
x
x
x

 



79 7 19
77
716 19
xx
xx
x
5
5
5 22
2
2 -
2
79 7 19
99
71619
xx
xx
x
 



If an equation has variable terms on both
sides, eliminate one by adding or subtract-
ing an equivalent variable term on both
sides. Then solve the equation for the
remaining variable.
Simplifying Before You Solve
In an earlier example, I said there was
another way to solve the equation -3(x – 1)
= -27, and this is the moment to look at
that method. When you solve equations,
you want to be able to use those inverse, or
opposite, operations, and having parentheses
or extra terms can get in the way of that.
Before you begin the actual work of solving
an equation, you want to make the equation
as simple as possible. Focus on one side of
the equation at a time, and if parentheses or
other grouping symbols are present, remove
them. You can do this by simplifying the
expression inside the parentheses, by using
the distributive property, or occasionally,
by deciding that the parentheses are not
necessary and just removing them. In the
equation -3(x – 1) = -27, you can distribute
the -3 and the equation will become -3x + 3
= -27. In the equation (5x + 2) + (3x – 4) =
14, the parentheses are really not necessary,
so you can just drop them and the equation
becomes 5x + 2 + 3x – 4 = 14.
Once parentheses have been cleared, take
the time to combine like terms (and only like
terms) before you begin solving. Each side
of the equation should have no more than
one variable term and one constant term
when you begin to solve. So in the equation
5 x + 2 + 3x – 4 = 14, you should combine
the 5x and 3x and combine the +2 and the
-4. The equation becomes 8x – 2 = 14.