This document defines and provides examples of linear equations in one variable. It explains that a linear equation is an equation that can be written in the form ax + b = c or ax = b, where a, b, c are constants and a ≠ 0. Examples of linear equations given include 3x + 9 = 0 and 7x + 5 = 2x - 9. The document also discusses how to determine if a value is a solution to a linear equation by substitution and simplification. Steps for solving linear equations are provided, which include isolating the variable using inverse operations like addition/subtraction and multiplication/division.

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3. Equation
• Equation- a mathematical expression
that states that two (2) quantities
are equal
• ** Use the equal sign (=) **
• ex. 2 + 8 = 10 ex. 10 – 5 = 5

4. Type of Equation
• Linear Equation in one variable-
equation that can be written in the
form . . .
• ax + b = c or ax = b
• where a, b, c are constants and a 0
•
• ex. 3x + 9 = 0 ex. 7x + 5 = 2x – 9
• ex. 4(x – 2)= 6 ex. x = 6
≠

5. • Linear Equation = First degree
equation
• ** First degree because the highest
power on the variable is one. **

6. Solution to a Linear
Equation
• Solution- the value that can be
substituted for the unknown
variable so the resulting statement
is true
• Solution Set- the set of all
solutions

7. To determine if a value is a
solution?
1. Substitute the value in for the
unknown variable.
2. Simplify both sides of the equation.
3. Does it make a true statement (both
sides of the equation are equal)?
• If yes, then the value is a
solution.
• If no, then the value is not a

8. For example . . .
ex. 4 is a solution to 3x – 5
= 7
3x – 5 = 7
3(4) – 5 = 7
12 – 5 = 7
7 = 7
True Statement
ex. 2 is not a solution to 5x –
9 = 6
5x – 9 = 6
5(2) – 9 = 6
10 – 9 = 6
1 = 6
False Statement

9. Determine if the numbers are
solutions to the following
equations.
• ex. ½ ; 2y + 5 = 4 • ex. 3 ; 4x + 3 = 18
– x

10. How to Solve Linear
Equations
• Isolate the variable on one side of the
equation so that the number that is the
solution is on the other side.
Typically
variable left-hand side
solution right-hand side
**But it does not matter which side is which

11. To isolate the variable use
Inverse Operations
Inverse Operations- Operations that
undo each other.
• Addition and Subtraction are inverse
operations.
• Multiplication and Division are
inverse operations.

12. Steps To Solve Linear
Equations
1. Simplify both sides of the equation as much as possible
• Clear Fractions
• Combine like terms
• Use distributive property
– 3(x + 5)
1. Move all variable terms to one side of the equation and
all constant terms to the other side of the equation
• Variables-left side of equation, Constants-right
side of equation
• Use addition or subtraction (Do opposite of what is
given)
1. Isolate variable (make the coefficient 1) on one side of
equation and solution on the other side
• Use multiplication or division (Do opposite of what
is given)
1. Check that your solution is correct by substituting it back