1. Solving One-Step Equations
Lesson 1.2.3

2. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
California Standard:
Algebra and Functions 4.1
What it means for you:
You’ll learn how to solve an equation to find out the value of an unknown variable.
Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
Key Words:
solve
isolate
inverse

3. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Solving an equation containing a variable means finding the value of the variable.
5 + x = 12
x = 7
It’s all about changing the equation around to get the variable on its own.

4. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Do the Same to Both Sides and Equations Stay True
The equals sign in an equation tells you that the two sides of the equation are of exactly equal value.
So if you do the same thing to both sides of the equation, like add five or take away three, they will still have the same value as each other.
4 + 6 = 9 + 1
Original, balanced equation. =
Add 5 to both sides.
15 = 15
Then simplify.
All three are balanced equations.

5. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
You Can Use This to Find the Value of a Variable
To get a variable in an equation on its own you need to do the inverse operation to the operation that has already been performed on it.
If a variable has been multiplied by a number, divide both sides by the same number. × ® ÷
If a variable has been divided by a number, multiply both sides by the same number. ÷ ® ×
If a variable has had a number added to it, subtract the same number from both sides. + ® –
If a variable has had a number subtracted from it, add the same number to both sides. – ® +

6. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
For example, solve the equation y – 5 = 33.
y has had 5 subtracted from it.
y – 5 = 33
So add 5 to both sides.
y – =
Do the additions to simplify both sides.
y + 0 = 38
You’ve got the variable alone on one side of the equation, so now you know its value.
y = 38

7. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Reverse Addition by Subtracting
When a variable has had something added to it, you can undo the addition using subtraction.

8. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Example 1
Find the value of x when x + 15 = 45.
Solution
x + 15 = 45
Write out the equation
x + 15 – 15 = 45 – 15
Subtract 15 from both sides
x = 30
Simplify to find x
Solution follows…

9. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Reverse Subtraction by Adding
When a variable has had something taken away from it, you can undo the subtraction using addition.

10. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Example 2
Find the value of k when k – 17 = 10.
Solution
k – 17 = 10
Write out the equation
k – =
Add 17 to both sides
k = 27
Simplify to find k
Solution follows…

11. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Example 3
Find the value of g when –10 = g – 9.
Solution
–10 = g – 9
Write out the equation
– = g – 9 + 9
Add 9 to both sides
–1 = g
Simplify to find g
Solution follows…

12. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Guided Practice
Find the value of the variable in Exercises 1–8.
1. x – 7 = 14
3. f + 13 = 9
5. y – 14 = 30
= 9 + v
x = 21
2. 70 = t + 41
4. g – 3 = –54
6. 22 = 14 + d
8. –6 = b – 4
t = 29
f = –4
g = –51
y = 44
d = 8
v = –4.5
b = –2
Solution follows…

13. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Reverse Multiplication by Dividing
When a variable in an equation has been multiplied by a number, you can undo the multiplication by dividing both sides of the equation by the same number.
y has been multiplied by 2.
2y = 18
So divide both sides by 2.
2y ÷ 2 = 18 ÷ 2
Do the divisions to simplify both sides.
y = 9

14. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Example 4
Find the value of b when 20b = 100.
Solution
20b = 100
Write out the equation
20b ÷ 20 = 100 ÷ 20
Divide both sides by 20
b = 5
Simplify to find b
Solution follows…

15. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Reverse Division by Multiplying
When a variable in an equation has been divided by a number, you can undo the division by multiplying both sides of the equation by the same number. d 2
d has been divided by 2.
= 50 d 2
So multiply both sides by 2.
• 2 = 50 • 2
Do the multiplications to simplify both sides.
d = 100

16. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Example 5
Find the value of t when t ÷ 4 = 6.
Solution
t ÷ 4 = 6
Write out the equation
t ÷ 4 • 4 = 6 • 4
Multiply both sides by 4
t = 24
Simplify to find t
Solution follows…

17. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Guided Practice
Find the value of the variables in Exercises 9–16.
9. 3k = 18
11. h ÷ 5 = –3
13. q ÷ 8 =
15. d ÷ –2 = –4
k = 6
10. b ÷ 3 = 4
12. –9y = 99
14. 10t = –55
= 8m
b = 12
h = –15
y = –11 1 2
q = 4
t = –5.5
d = 8
m = 30
Solution follows…

18. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Independent Practice
1. The Sears Tower in Chicago is 1451 feet tall, which is 405 feet taller than the Chrysler Building in New York. Use the equation C = 1451 to find the height of the Chrysler Building.
Find the value of the variable in Exercises 2–7.
2. k + 7 = 10
4. s + 4 = –7
6. h + 0 = 14
1046 feet
k = 3
3. c + 10 = –27
5. 70 = 5 + b
7. 32 = 11 + a
c = –37
s = –11
b = 65
h = 14
a = 21
Solution follows…

19. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Independent Practice
8. The Holland Tunnel in New York is 342 feet longer than the 8216-foot-long Lincoln Tunnel. Use the equation H – 342 = 8216 to find the length of the Holland Tunnel.
Find the value of the variable in Exercises 9–14.
9. x – 7 = 13
11. p – 13 = –82
= g – 18
8558 feet
= m – t – 27 = –7 = y – 2
x = 20
m = 76
p = –69
t = 64
g = 118
y = –5
Solution follows…

20. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Independent Practice
15. Marlon buys a sweater for $28 that has $17 off its usual price in a sale. Write an equation to describe the cost of the sweater in the sale compared with its usual price. Then solve the equation to find the usual price of the sweater.
Find the value of the variable in Exercises 16–21.
16. 5c = 80
18. 22x = –374
20. –3k = –24
x – 17 = 28, x = $45
c = 16
17. v ÷ 7 = 3
19. h ÷ –2 = 4
21. –27 = f ÷ 3
v = 21
x = –17
h = –8
k = 8
f = –81
Solution follows…

21. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Independent Practice
22. The tallest geyser in Yellowstone Park is the Steamboat Geyser. Reaching a height of 380 feet, it is twice as high as the Old Faithful Geyser. Use the equation 2F = 380 to find the height reached by the Old Faithful Geyser.
190 feet
Solution follows…

22. Solving One-Step Equations
Lesson
1.2.3
Solving One-Step Equations
Round Up
Solving an equation tells you the value of the unknown number — the variable.
To solve an equation all you need to do is the reverse of what’s already been done to the variable. That way you can isolate the variable.
Just remember that you need to do the same thing to both sides. That’s what keeps the equation balanced.