This document provides examples and explanations for solving one-step equations involving addition, subtraction, multiplication, and division. It also gives examples of writing and solving equations to solve word problems. Key steps include defining a variable, writing an equation, solving the equation, and answering the question. Common language in word problems like "is", "of", and "per" indicate the operation to use when writing the equation.

2. 1-step Equations: + and – 9/23/13
In elementary school, you solved
equations that looked like this:
In Algebra, we just use a variable
instead of the box!
We could rewrite the same
equation like this: x + 3 = 5

3. To solve:
Need to get x by itself.
We must “undo” whatever has been
done to the variable.
Do the same to BOTH SIDES of the =
sign!
Answer should be: x = some number.

4. Equations Have to Balance!
Both sides of the = sign must “weigh”
the same!
When you change one side, do the
same to the other side, so it stays
balanced!
x + 3 = 7

5. Examples:
Solve each equation. Check your
answers!
x + 3 = -7 m – 6 = 8

6. 3.4 + a = 0.5
y – 1.3 = -3.9

7. 1/4 = 1/2 + t
-2/5 = x – 1/3

8. You Try!
Solve each equation. Check your
answers!
x – 9 = -6 1.6 + n = 10.7

9. 1-step Equations: × and ÷ 9/24/13
Just like with adding and
subtracting, we need to “undo” what is
done to x.
Use division to “undo” multiplication.
Use multiplication to “undo” division.
Remember: A fraction bar means
divide!
Example: says x divided by 3!

10. Examples:
Solve each equation:
2x = 8
12.9 = -3.2b

12. You Try!
Solve each 1-step equation.
-4.2a = 16.6

13. Applications 9/26/13
How to solve a word problem using a
linear equation:
1. Write a verbal model
2. Define a variable for the unknown
3. Write an equation
4. Solve
5. Answer the question in sentence form

14. Common Language:
In a word problem:
“is” means =
“of” means multiply
“per” means multiply
“less than” usually means subtract
“more than” usually means add

15. Example 1
Paula has 3 more dolls than her friend
Briana. If Paula has 10 dolls, write and
solve an equation to find out how many
dolls Briana has.
Let be
Paula’s
dolls
Briana’s
dolls
+ 3=
Briana’s dollsb
10 = b + 3

16. You Try!
A used book costs $17 less than the
same book new. The used book costs
$9. Write and solve an equation to
find out how much the new book cost.

17. Example 2
The melting point of bromine is of the
melting point of nitrogen. The melting point
of bromine is −7 C. Write and solve an
equation to find the melting point of
nitrogen.
Let be the
Melting
point of
bromine
1/30
Melting
point of
nitrogen
=
Melting point of nitrogenn
-7 = 1/30 n

18. You Try!
The melting point of mercury is about
of the melting point of krypton. The
melting point of mercury is −39 C. Write
and solve an equation to find the melting
point of krypton.

19. Example 3
John earns $5 per hour mowing
lawns. Write and solve an equation to
find how many hours he must work to
earn $40.
Let be the
Amount
earned $5
# of
hours=
# of hoursh
40 = 5 h

20. You Try!
If you save at a rate of $15 per month,
how long will it take you to save $135?
Write and solve an equation.