Download RETAKE REVIEW Evaluating Expressions and Solving Equations

RETAKE REVIEW
Evaluating Expressions and Solving Equations Summative
Translate each mathematical statement.
Study Tip! For additional review, read through 1.3 and 1.4 in your textbook and rework
homework problems from those sections.
1. Three less a number is negative forty.
3 – x = -40
2. Five less than twice a number is the difference of half the number and two.
2x – 5 =
3. Five more than the product of ten and a number is eighty.
5 + 10x = 80
4. The quotient of three times a number y and six. Then, evaluate if y = 16
;8
5. Seven times the difference of twelve and a number x. Then, evaluate if x = -4.
7(12 – x) ; 112
Evaluate the given expressions.
Study Tip! If you are struggling with these, remind yourself to use the order of
operations by writing the word PEMDAS next to each question. If you would like
additional practice see section 1.2 in your textbook.
6. -12 ÷ (5-7)2 + 3 • -6
-21
8.
-5
(-15 + 5)2 – 50__
24 ÷ 23 – (52 – 12)
7. 200 – 2a2 if a = -9
38
9. [(b – a)3 – (a + 4)2]3 if a = 1 and b = 4
8
Simplify using the distributive property.
Study Tip! Remember to distribute and combine like terms. Watch the negative! For
extra examples and practice problems see section 2.5 of your textbook.
10. -6(3y – 8)
-18y + 48
11. – (4w + 7z)
-4w – 7z
12. (3 – 6y) – 4(2 + 2y)
13. -36x² + 18x – 24
6
-6x2 + 3x – 4
-14y – 5
Solve each equation. Show your work!
Leave all answers as integers or fractions.
Study Tip! Start by distributing and combining like terms. Remember to isolate the
variable on one side the equals sign. Don’t forget, whatever you do to one side of the
equation, you have to do to the other side of the equation. Watch out for negatives! For
extra examples and practice problems see sections 3.1 – 3.6 in your textbook.
14. 12 = x + 19
15. x + (-5) = -15
x = -7
x = -10
16. 20y = 5
17. x = 18
y=
x = 27
18. 7 – y = -11
19. ¼(8y + 12) = -3
y = 18
y=3
20. –2(4 – x) = -40
21. 2(3x + 5) = 66 – 22x
x = -16
x=2
22. –2x – 6 = 5x + 8
23. 4(1 – x) + 3x = -2(x + 1)
x = -2
x = -6
24. ¼(12x + 16) = 10 – 3(x – 2)
25. -2y + 3(4 – y) = 12 – 5y
x=2
All Real Numbers ( )
26. 5(2 – x) + 7x = -3(x + 5)
27.
x = -5
x = -6
28. 3 =
45
x-2
11x + 6
29.
x=9
x = 15
(27x + 18) = 12 + 6(x – 4)
2x +5 = 7
x
3
Properties and using properties to justify the steps of an equation.
Study Tip! If you struggle to identify the properties, you may want to consider making
flashcards to help you study. Look back at your notes, homework assignments, and
past assessments. Try covering up the justifications with a piece of paper and quizzing
yourself.
30. Give a mathematical example for each of the following properties:
a. Reflexive x = x
b. Transitive x = y and y = 100 so x = 100
c. Multiplication Property of Zero -9 • 0 = 0
d. Associative (x + 3) + 2 = x + (3 + 2)
e. Commutative x3 = 3x
31. Fill in the property that justifies each step.
5 + 16 = 3(x – 5)
3(x – 5) = 5 + 16
Given
Symmetric Property
3(x – 5) = 16 + 5
Commutative Prop. Of Addition
3x – 15 = 16 + 5
Distributive Property
3x – 15 = 21
Substitution
3x – 15 + 15 = 21 + 15
Addition Property of Equality
3x + 0 = 36
Additive Inverse
3x = 36
Additive Identity
Multiplicative Property of Equality
1x = 12
Multiplicative Inverse
x = 12
Multiplicative Identity
Study tip – Go back and redo any missed questions on your old HW assignments and
assessments! Reworking the problem and arriving at the correct answer (which you
hopefully wrote down when we went over it in class) will help you prepare for the retake.