Section 2.1
Linear Equations in One Variable
Personal Info
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Dr. Green
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Undergraduate in Secondary Ed. – Math
Masters in Math Ed.
Ph.D. in Pure Mathematics
Varying experience with many age groups
General Expectations
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Summer is fast!!!
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Think of me as a “stickler.”
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Learning is a two-way street.
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15% / 85%
Syllabus
Expressions and Equations
An expression does not have an equal
sign.
 An equation does.
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Linear Equation in One Variable
A linear equation in one variable can be written in the form
𝐴𝑥 + 𝐵 = 𝐶
where 𝐴, 𝐵, and 𝐶 are real numbers, with 𝐴 ≠ 0.
Example 1
Determine if the following are equations or
expressions.
a.
−3𝑥 + 2 − 4 − 𝑥 = 4
b.
4 𝑥 + 3 − 5𝑥 2 + 28
c.
4 = 18𝑥 3 + 5𝑥
Example 2
Are the equations below linear in 𝑥?
a. 5𝑥 + 4 𝑥 = −2
b.
7 = 𝑥 + 3𝑥
c.
27 = 𝑥 3
5
d.
𝑥
+ 23 = 31
Two Equation-Solving Illustrations
Example 3
Solve.
a.
7𝑥 − 4 = 31
b.
−4𝑡 + 5𝑡 − 8 + 4 = 6𝑡 − 4
c.
−2𝑘 − 3 4 − 2𝑘 = 2 𝑘 − 3 + 2
Possible Solutions
When solving these types of equations,
there are three possibilities.
Type
Number of
Examples
Solutions
Conditional
One
Identity
Infinite
Contradiction None
Write
𝑥 = −9
{−9}
6=6
{all real numbers}
−2 = 1
{∅}
Example 4
Solve.
a.
−2 𝑥 + 3 − 7 = 5𝑥 − 7𝑥
b.
6𝑡 + 2𝑡 − 4 = 16
1
𝑡
2
c.
- 6𝑚 − 4𝑚 + 8
= 9 + 6𝑚 + 3
−
1
4
Example 5
Solve.
a.
5−
𝑛
b.
5
2
𝑥
3
= 12
𝑛
4
− =2
3
c. 𝑡
4
−
2𝑦+5
d.
5
1
𝑡
3
=
=
5
𝑡
6
−5
3𝑦+1
−𝑦+7
+
2
2
Example
Solve.
a.
0.08𝑥 + 0.12 260 − 𝑥 = 0.48𝑥
b.
0.006 𝑚 + 2 = 0.07𝑚 + 0.009
Questions???
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