Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 10: Solving Equations and Inequalities 125

Solving an equation is undoing what was
done by doing the opposite and stripping
away the layers of arithmetic. To accomplish
that, you need to undo things in the reverse
of the order in which they were done. You
undo the last bit of arithmetic first and work
backward. Think about putting on your
shoes and socks. You put a sock on first,
then the shoe. But to take off your shoes and
socks, you take the shoe off first, then the
sock. It really wouldn’t work in the other
order.

To solve a two-step equation, take a
moment to think about what was done to
the variable. Notice what operations were
performed and in what order. Then perform
the opposite, or inverse, operations in
the opposite order. So if you see that the
variable was multiplied by 4 and then 9 was
subtracted, you’ll add 9 and then divide by

4. Let’s look at some examples.

Solve 5x – 11 = 5

Look at the equation and map out what
happened to the variable. The number
represented by x was multiplied by 5 and
then 11 was subtracted from the result.
The answer was 5. So what happened was
multiplication by 5, then subtraction of 11.
The opposite of multiplication is division
and the opposite of subtraction is addition,
but you also want to reverse the order. Your
plan for solving the equation will be first to
add 11, then to divide by 5.

Add 11 to both sides.

511 5
11 11
516

x

x







Then divide both sides by 5.

You can check your solution of x = 3.2 by

substituting 3.2 into the equation to see if

it makes a true statement. 5(3.2) – 11 = 5

becomes 16 – 11 = 5, which is true, so your

solution is correct.

Here’s another example, with some different

operations.

Solve t

4

37 

In this equation, t is divided by 4, and then

3 is added, so the plan will be to subtract 3

and then multiply by 4. Take it one step at

a time.

Subtract 3 from both sides of the equation.

Then multiply both sides of the equation

by 4.

Check the solution. Is^16

4

37  a true

statement? It is, so the variable t does

represent 16.

516

5

5

16

5

32

x

x

x

.







t

t

4

37

33

4

4

5 --

51

5