This document provides an overview of linear equations and how to solve them. It defines key characteristics of linear equations, such as variables only having an exponent of 1 and no terms being multiplied together. Various examples of linear and non-linear equations are shown. The document then explains that solving linear equations involves finding the value of the variable that makes both sides equal. It provides step-by-step instructions for solving one-step equations and works through examples of solving multi-step equations. Students are given a checkpoint to practice solving equations on their own before moving to an independent practice section.

1. SOLVING LINEAR
EQUATIONS
Algebra 1 Mr. Saucedo

2. Objective
 Learn how to identify linear equations.
 Learn tricks to solve linear equations.

3. True facts about linear
equations
 The variables will always have 1 as exponent.
 Linear equation = linear function
 Two variables will never be multiplied.
 The graph of a linear equation is always a line.
 Y = mx + b is called the equation of a line in
slope-intercept form.
 The y can be replaced with f(x).
 Example: y = 3x + 2 is the same as: f(x) = 3x + 2.

4. Examples.
Linear equations Non linear equations
2x + 5 = -8 7a + b2
= 3
X = 9 y = 1/x
Y = .5x x + xy = 1
6s – 3t = 8 5+= xy

5. State whethereach function is a linearfunction. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10
m = – 5, b = 1 0
b) g(x) = x4
– 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy No!
Two variables are multiplied together.
Linear EquationsLinear Equations

6. Is it a linear equation?

7. NOTES:
SOLVING THE LINEAR
EQUATIONS
Solving linear
equations means
finding the value of
the variable that
makes the equation

8. SOLVING LINEAR EQUATIONS:
ONE STEP EQUATIONS
THERE IS ONE THING TO REMEMBER:
WHAT YOU DO TO ONE SIDE OF THE
=
YOU DO TO THE OTHER!!!

9. GUIDED PRACTICE
Solve:
3)128(
4
3
=−x 54)5(3 +=−− xx

10. Guided Practice
Solve
34)36(
3
2
+=+ xx 161.0)84.0(27. −−=+− nn

11. CHECKPOINT
 Solve )3(4)13(2 +=+− xx

12. Checkpoint
 Solve xx +=+−− 7)2(2

13. Independent practice
 Solve the following equations.
1. -5(4v – 3) = 175
2. 205 = -8(4x – 1) + 5
3. -7(7 + x6x) + 4x = -201
4. 3 – 5n = 3(1 – 6n)
5. -7k + 27 = 3(1 – 6k) + 8k
Answers: 1. -8, 2. -6, 3. 4, 4. 0, 5. -8, 6. -14