1. CHAPTER 3
TEST
REVIEW

2. a(b + c) = ab + ac (b + c)a = ab + ac THE DISTRIBUTIVE PROPERTY:
GOAL: Use the distributive property to write algebraic expressions
a(b + c) = ab + ac
(b + c)a = ab + ac

3. Examples:
7(x + 9)
6(y – 4)
-12(x + 5)
-2(y – 3)
-(x + 6)
(a – 3)8
(y – 10)(-2)
(z + 12)8

4. 7(a + b)
(x – y)(-3)
7(2x + 5y)
-2(4a – 6b)
(2x + 9y)4

5. 5x + 13 – 9x + 7 SIMPLIFYING ALGEBRAIC EXPRESSIONS:
GOAL: USE THE DISTRIBUTIVE PROPERTY TO
SIMPLIFY ALGEBRAIC EXPRESSIONS.
5x + 13 – 9x + 7
x is called the variable in the above expression
5 and -9 are called the coefficient of the variable x
13 and 7 are called constants (the terms that have no variable)
5x and 9x are called like terms since they have the same variable
13 and 7 are called like terms since they are both constants

6. COMBOINING LIKE TERMS:
2x x
8y – y
-6a a
15 + 3b – 10
7k – k + 19
-x x – 1 + x – 7

7. 5(x – 5) + 7
2(a + 6) – 8
-7(3a – 1) + 14a
-10(y + 2) + 15a

8. FINDING THE PERIMETER:
5x + 7 1.
2x – 1
2x + 5 2.
4x +2
x – 2

9. x + 9 = 23 - 9 -9 x = 14 SOLVING EQUATIONS BY ADDING AND SUBTRACTING
Goal: Solve equations by using the subtraction and
addition properties of equality.
x + 9 = 23
x = 14

10. SOLVE:
6. x + (-12) = 17
7. y + (-10) = - 37
8. a + (- 9) = 14
9. a – (-12) = 19
10. x – (-34) = 74
x + 15 = 19
a + 18 = - 7
y + 7 = 45
4. x – 13 = -8
5. v – 6 = 13

11. 5x = 35 5 5 x = 7 Solving Equations by Multiplying or Dividing
Goal: Solve equations using the division and
multiplication property of equality.
5x = 35
x = 7

12. –x = 15
-y = -25
-t = 98
-w = -123
-p = -78

13. Solve: SHOW ALL WORK
6a = 42
-3b = 99
9z = 144
-7y = -84
10x = 70

14. x
7 ●
= 8
● 7 7
x = 56

15. − 𝑤 5 =6
𝑥 7 =−9
𝑡 12 =−4
− 𝑦 12 =10
𝑔 40 =80

16. 4x + 17 = 37 -17 -17 4x = 20 4 4 x = 5 Solving Two-Step Equations
Goal: Solve two-step equations
4x + 17 = 37
4x = 20
x = 5

17. Examples:
5x + 12 = 72
4y – 16 = 12
-2a + 15 = -11
4. 9x – 16 = 20
5. -12x + 34 = 46
6. -10y – 5 = 35

18. 𝑥 = 8
𝑤 −4 − 10 = -4
3. 𝑦 = 24
4. 𝑥 7 − 14 = -6

19. Six more than twice a number is -20.
Writing Two-Step Equations
Goal: write verbal sentences as two-step equations,
solve verbal problems by writing and solving
two-step equations.
Six more than twice a number is -20.

20. Examples:
Seven more than three times a number is 31. Find the number.
The quotient of a number and 5, increased by 8, is equal to fourteen.
Find the number.

21. Using Formulas Goal: Solve problems by using formulas, solve
problems involving the perimeters and
areas of rectangles.
A formula is an equation that shows a relationship among certain quantities.
Examples:
1. D = RT 2. A = BH 3. A = lw 4. P = 2l + 2w

22. Examples using the Distance Formula
What is the rate in miles per hour of a dolphin that travels 120 miles in 4 hours?
How long will it take you to drive 480 miles if you drive 60mph?
If you drive 55mph for 7 hours how far have you traveled?

23. Area and Perimeter of a Rectangle Formula
What is the area and perimeter of a rectangle with length of 5ft and a width of 3ft?
Find area and perimeter of each rectangle. 2.
6ft
9ft 3.
8cm
13cm

24. Word Problems:
1. The perimeter of a rectangle is 30ft. Its width is 5cm, what is its length?
2. The area of a rectangle is 63in2. Its length is 9in, what is its width?

25. PRACTICE
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