Module 1 Lesson 2

A Literal Equation is an equation with two or

more variables.•You can "rewrite" a literal equation to isolate any one of the variables using inverse operations.

•When you rewrite literal equations, you may have to divide by a variable or variable expression.

Step 1 Locate the variable you are asked to

solvefor in the equation.

Step 2 Identify the operations on this

variable and the order in which they are applied.

Step 3 Use inverse operations to undo

operationsand isolate the variable.

A. Solve x + y = 15 for x.x + y = 15 Since y is added to x, subtract y

from both sides to undo the addition.

–y –yx = –y + 15

B. Solve pq = x for q. pq = _x_ p p

Since q is multiplied by p, divide both sides by p to undo the multiplication.

Solve 5 – b = 2t for t.5 – b = 2t Locate t in the equation.

Since t is multiplied by 2, divide both sides by 2 to undo the multiplication.

Solve for the indicated variable.

1.

2.

3. 2x + 7y = 14 for y

4.

P = R – C for C

for m

5. for C

for h

1. H = 3V

A

2. y = 14 – 2x

7

3. C = R – P

4. m = x(k – 6 )

5. C = Rt + S

Locate d in the equation.

The formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol in your answer.

Now use this formula and the information given in the problem.

Since d is multiplied by , divide both sides by to undo the multiplication.

Now use this formula and the information given in the problem.

The bowl's diameter is inches.

The formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol in your answer.

Every Real Number is either rational or irrational.

We refer to these sets as subsets of the real numbers, meaning that all elements in each subset are also elements in the set of real numbers.

Numbers Examples

Natural Numbers 2,3,4,17

Whole Numbers 0,2,3,4,17

Integers -5,-2,0,2,5

1 5 1 2Rational Numbers , ,.4 ,0,.6

2 1 5 3

Irrational Numbers 2, , 3

25 is a rational number because 25 5.

Example

13, 0, , .95, , 8, 16

2

Consider the following set of numbers.

List the numbers in the set that are:

a. Natural Numbers

b. Whole Numbers

c. Integers

d. Rational Numbers

e. Irrational Numbers

f. Real numbers

Example

13, 0, , .95, , 8, 16

2

Consider the following set of numbers.

List the numbers in the set that are:

a. Natural Numbers: √16 = 4, so that is the only Natural Number

b. Whole Numbers: 0 , √16

c. Integers: -3, 0, √16

d. Rational Numbers: -3, 0, ½ , .95, √16

e. Irrational Numbers: √8

f. Real numbers: All of the numbers listed above!

Property Addition Multiplication

Commutative a + b = b + a ab = ba

Associative (a + b) + c = a + (b + c) (ab)c = a(bc)

Identity a + 0 = a a * 1 = a

Inverse a + (-a) = 0 a * 1/a = 1

Distributive a(b + c) = ab + ac

Rules:Commutative Property of

Addition

a+b = b+a

Commutative Property of Multiplication

ab = ba

It doesn’t matter how you swap addition or multiplication around…the answer

will be the same!

Samples:Commutative Property of

Addition

1+2 = 2+1

Commutative Property of Multiplication

(2x3) = (3x2)

Rules:Associative Property of

Addition

(a+b)+c = a+(b+c)

Associative Property of Multiplication

(ab)c = a(bc)

It doesn’t matter how you group (associate) addition or multiplication…

the answer will be the same!

Samples:Associative Property of

Addition

(1+2)+3 = 1+(2+3)

Associative Property of Multiplication

(2x3)4 = 2(3x4)

Rules:Identity Property of Addition

a+0 = a

Identity Property of Multiplication

a(1) = a

Samples:Identity Property of

Addition

3+0=3

Identity Property of Multiplication

2(1)=2

What can you add to a number & get the same number back? ZERO

What can you multiply a number by and get the number back? ONE

Rules:Inverse Property of Addition

a+(-a) = 0

Inverse Property of Multiplication

a(1/a) = 1

Samples:Inverse Property of

Addition

3+(-3)=0

Inverse Property of Multiplication

2(1/2)=1

Think opposites! The Inverse property uses the inverse operation to get to the identity!

Rule:a(b+c) = ab+bc

Samples:4(3+2)=4(3)+4(2)=12+8=20

• 2(x+3) = 2x + 6• -(3+x) = -3 - x

You can distribute the coefficient through the parenthesis with multiplication and remove the

parenthesis.

1. 6 + 8 = 8 + 62. 5 + (2 + 8) = (5 + 2) + 83. 12 + 0 =124. 5(2 + 9) = (5 2) + (5 9)5. 4 (8 2) = (4 8) 26. 5/9 9/5 = 17. 5 24 = 24 58. 18 + -18 = 0 9. -34 1 = -34

1. Commutative2. Associative3. Identity4. Distributive5. Associative6. Inverse7. Commutative8. Inverse9. Identity

All real numbers have closure.

The Closure property states the if a and b

are real numbers then: • a + b is a real number• ab is a real number.

So, if you add two rational numbers, your sum

will be rational. Also, if you add two irrational

numbers, that sum will be irrational.