Linear Equations in One Variable

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

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

Linear Equation = First degree equation

** First degree because the highest
power on the variable is one . **

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

Used to show solution set { }

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
solution.

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

Determine if the numbers are
solutions to the following
equations.

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 **

Think of = sign as a scale that
keeps everything balanced

* What you do to one side you must do to the
other in order to keep the equation balanced *

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)

2. 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)

3. 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)

4. Check that your solution is correct by substituting it
back into original equation to see if it makes a true
statement (both sides equal the same value)

How to remember rules !

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