INTRODUCTION TO ALGEBRAIC EQUATION
Identification:
It is a statement of the equality of two expressions.
Algebraic Equation
Identification:
It makes a statement about the relationship between two expressions.
Mathematical Sentence
This property states that an equation can be written in two ways, with both sides interchanged (flipped).
Symmetric Property of Equality
Modified True or False:
Linear Equations are equations that contain several variables.
False (Literal)
Identification:
It can be written in the form ax + b = 0, where a and b are real numbers and a should not be equal to 0.
Linear Equation in One Variable
Who invented the equal sign in 1557?
Robert Recorde
Which of the following is NOT a mathematical sentence?
A. Equation
B. Expression
C. Inequality
B.
Identify the property illustrated below:
If a=b and b=c, then a=c.
Transitive Property
The following are examples of literal equations EXCEPT
A. d=st
B. V=s2h
C. x+16 =3 (x+2)
D. s + t = s +t
C
Identification:
It is an equation that is true for some value(s) of the variable(s) and not true for others.
Conditional Equation
Modified True or False:
Inequalities show that two expressions are equal.
FALSE (not equal)
Which of the following is NOT a mathematical sentence?
A. x = 5
B. x + 5 = 10
C. 5x > 10
D. x2 + 5x + 10
D
Identify the property illustrated below:
If 2x=16, then x=8.
Division Property of Equality
Solve for l:
A=lw
l=A/w
Identify the (a) type of equation and the (b) number of solution/s of the equation below:
5 (n+2) = 5n + 10
(a) Identity Equation
(b) infinitely many solutions (all real numbers)
Multiple Choice:
Which of the following is an example of an algebraic equation?
A. 5x + 10
B. x + 5 = 10
C. 5x > 10
D. x2 + 5x + 10
B
Give the mathematical sentence:
Nine times the sum of a number m and 3 is 45.
9 (m+3) = 45
Fill in the blanks:
If 7n - 3 = 25, then 7n = _____.
28
Solve for h:
V = πr2h
h = V/πr2
Identify the (a) type of equation and the (b) number of solution/s of the equation below:
2w + 3 = 2w
(a) False Equation
(b) No solution
Multiple Choice:
Which of the following is an example of an algebraic inequality?
A. 5x + 10
B. x + 5 = 10
C. 5x > 10
D. x2 + 5x + 10
C
Give the English translation:
3x - 5 = 4
5 less than thrice the number x is 4.
When you arrive at this equation: 5 (x + 3) = 20, which of the following property will you use next?
A. Addition Property of Equality
B. Distributive Property
C. Substitution Property
D. Subtraction Property of Equality
B
Solve for x:
4y = 2x
x=2y
Give what is asked:
Given: The sum of three consecutive even integers is 108.
(a) What is the representation of the second integer?
(b) What is the working equation?
(c) What are the integers?
(a) Let x+2 = the second even integer
(b) x + (x+2) + (x+4) = 108
(c) 34, 36, and 38