Use this PowerPoint to review Linear Equations in preparation to your Unit 3 Test.

1. Linear Equations
and Inequalities

2. Properties of Equality
If a = b, then a + c = b + c.
Multiplication Property of Equality
If a = b, then a – c = b – c.
Addition Property of Equality
If a = b, then a × c = b × c.
Division Property of Equality If a = b, then a ÷ c = b ÷ c.
Subtraction Property of Equality
Let a, b, and c be real numbers.

3. Properties of Operations
a + b = b + a
Distributive Property
(a + b) + c = a + (b + c)
Commutative Property
a × (b + c) = (a × b) + (a × c)
Associative Property
a × b = b × a
(a × b) × c = a × (b × c)
a × (b – c) = (a × b) – (a × c)

4. Properties of Inequality
Multiplication Property of
Inequality
Addition Property of
Inequality
Division Property of
Inequality
Subtraction Property of
Inequality
If a > b, c > 0, then a ÷ c > b ÷ c.
If a > b, c < 0, then a ÷ c < b ÷ c.
If a < b, c < 0, then a ÷ c > b ÷ c.
If a < b, c > 0, then a ÷ c < b ÷ c.
If a > b, c > 0, then a × c > b × c,
If a > b, c < 0, then a × c < b ×
c. If a < b, c < 0, then a × c >
b × c. If a < b, c > 0, then a ×
c < b × c.
What happens when you replace < with > or < or > in each of
these properties? Does the property still hold? Try it!
Let a, b, and c be real numbers.
If a > b, then a + c > b + c.
If a < b, then a + c < b + c.
If a > b, then a – c > b – c.
If a < b, then a – c < b –
c.

5. Linear Equations with One Variable
An equation can be either a true statement or a false statement.
Which of these equations are true statements?
3(4 + 5) = 27
12 – 3 = 3 – 12
8 + 2 = 9
9 + 1 = 10
6 × 5 = 5 × 6
42
= 8
An equation with a variable can be either a true statement or a
false statement, depending on the value given to the variable.
Which of these equations are true statements?
3(h + 5) = 27, h = 48 + x = 9, x = 1 6 × 5 = r × 6, r = 4
12 – 3 = 3 – m, m = –6y + 1 = 10, y = 8 42
= w, w = 8

6. Linear Equations with One Variable
An equation can be either a true statement or a false statement.
Which of these equations are true statements?
3(4 + 5) = 27
12 – 3 = 3 – 12
8 + 2 = 9
9 + 1 = 10
6 × 5 = 5 × 6
42
= 8
An equation with a variable can be either a true statement or a
false statement, depending on the value given to the variable.
Which of these equations are true statements?
3(h + 5) = 27, h = 48 + x = 9, x = 1 6 × 5 = r × 6, r = 4
12 – 3 = 3 – m, m = –6y + 1 = 10, y = 8 42
= w, w = 8

7. Solving Linear Equations with One Variable
When solving an equation, you find the value(s)
of the variable that makes the equation true.
Use your number sense to help you solve an equation with one variable.
y + 2 = 11
think
What number plus 2 equals 11?
next
Substitute the number you have chosen into the original
equation to check to see that it makes the equation true.
y + 2 = 11
9 + 2 = 11
11 = 11
Let y = 9.
Substitute 9 for y.
The equation is true for y = 9.

8. Solving Linear Equations with One Variable
Use properties to help you solve an equation with one variable.
y + 2 = 11
y + 2 – 2 = 11 – 2
y = 9
The solution checks.
Using the Subtraction Property of Equality,
subtract 2 from both sides of the equation.
Check the solution.
y + 2 = 11
9 + 2 = 11
11 = 11
Check:

9. Solving Linear Inequalities with One Variable
x – 4 > 2
x – 4 + 4 > 2 + 4
x > 6
Using the Addition Property of Equality,
add 4 to both sides of the equation.
Graph the solution on a number line.
x – 4 > 2
Use Properties to help you solve an inequality with one variable.
5 9-3 1 6 10-2 2-4 -1 0 3 4 7 8
x – 4 > 2
7 – 4 > 2
3 > 2
All values greater than 6 are solutions
to this inequality.
The solution checks.
Try x = 7.
Choose a value greater than 6 and check it.

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