Vocabulary Check: Define the following terms and provide examples (if it applies). This should be completed prior to attending the review livelesson.
∙ Absolute Value- the absolute value of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and |x| = −x if x is negative, and |0| = 0.
∙ Additive Inverse- additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite, sign change, and negation.
∙ Distributive Property- the distributive property of binary operations generalizes the distributive law from elementary algebra, which asserts that one has always
∙ Equation- equation is a statement that asserts the equality of two expressions, which are connected by the equals sign =
∙ Inverse Operations- Inverse operations are pairs of mathematical manipulations in which one operation undoes the action of the other—for example, addition and subtraction, multiplication and division. The inverse of a number usually means its reciprocal, i.e. x - 1 = 1 / x . The product of a number and its inverse (reciprocal) equals 1
∙ Isolate- Using inverse operations to undo addition, subtraction, multiplication, and division to get the variable alone
∙ Order of Operations- the order of operations is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression
∙ Variable a variable is a symbol which works as a placeholder for expression or quantities that may vary or change; is often used to represent the argument of a function or an arbitrary element of a set. In addition to numbers, variables are commonly used to represent vectors, matrices and functions
Simplify the expression. Make sure to include various key words you learned in this unit. Clearly list the steps in order so that anyone reading this can follow. Make sure to circle or highlight the simplified solution:
18 ÷ 3(-12 + (-2)3 – 7) + 16 answer -50
Find the solution to the equations below. Make sure to justify (support) your answer: - What is the solution to -25 + z = 8 z=33
- What is the solution to a + 4 = 71 a=67
- What is the value of 4 + 2(13 – 4) ÷ 3 =10
- What is the value of 6 * b = -84 b=-14
Unit 2 Integers and Algebraic Expressions Unit Review Study Guide - What is the solution to k/-7 = 10
Additive Inverse:
- What is the additive inverse of 54?
o -54
o 38
o – ( - |-54|)
o – ( - ( - (-54)
Inequalities:
- Which symbol will make |-5| <|7| true?
- Which symbol will make - |9| = 9 true?
Number Properties:
- What property is shown by 5( a + 6 ) = 5(a) + 5(6)? _______commtive property_________________ - Which property is shown by 4 + 8 = 8 + 4? _________associative property ___________________ - Which expression can be written as 3 * (5 + 2)?
o 3 * 2 + 5
o 3 * 5 + 2
o (3 + 5) + (3 + 2)
o (3 * 5) + (3 * 2)
Writing Equations:
How is the sentence 26 more than g is 8 written as an equation? ________________________________ Translate the following sentence in math symbols. Then solve the problem: a more than 6 is -30
Ordering real numbers:
List the following numbers in descending order: - |5|, -2, |-5|, -(- 7), 0
Unit 2 Integers and Algebraic Expressions Unit Review Study Guide This Photo by Unknown Author is licensed under CC BY-NC-SA
1. IF x = 14, which equation is true? Justify your answer!
A. 3(20 – x) = 44
B. 3(12 – x) = 6
C. 2(x – 3) = 22
D. 2x – 3 = 22
2. What is the solution to this equation? Make sure to show your work.
30.16 = 17.56 + 5x
A. 6.032
B. 3.512
C. 12.6
D. 2.52
1. IF x = 14, which equation is true? Justify your answer!
C. 2(x – 3) = 22
To justify the answer, substitute x = 14 into each equation and check if the equation holds true.
For equation C:
2(14-3) = 2(11) = 22
So, equation C is true when x = 14.
2. What is the solution to this equation? Make sure to show your work.
30.16 = 17.56 + 5x
Subtract 17.56 from both sides of the equation:
30.16 - 17.56 = 17.56 + 5x - 17.56
12.6 = 5x
Divide both sides of the equation by 5:
12.6/5 = 5x/5
2.52 = x
So, the solution to the equation is x = 2.52. The correct answer is D.