Download CHAPTER 2: Solving Linear Equations and Inequalities

MATH 0960
Section 2.4 Notes
CHAPTER 2: Solving Linear Equations and Inequalities
Section 2.4: Solving Linear Equations with a Variable on Only Side of the Equation.
Topics:
A. Solve linear equations containing only whole numbers.
B. Solve linear equations containing decimal numbers.
C. Solve linear equations containing fractions.
Preliminary: Solve linear equations with a variable on only one side of the equation.
 Combining the addition and multiplication properties of equations, you can solve
linear equations in the form
. First add or subtract to isolate the term
with the variable, then multiply or divide.
 This is what I call a “two-step equation.”
A. Solve linear equations containing only whole numbers.
 What does a problem look like?
Examples: Solve.
1)
Answer:
2)
Answer:

Note: in any problem with only whole numbers, if your final step does not result
in a whole number, just write it as a simplified fraction.
What do I need to know?
If the equation is not in the above form, each side should be simplified first.
Examples: Solve.
(
)
1)
Answer:
2)
(
)
Answer:
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MATH 0960
Section 2.4 Notes
B. Solve linear equations containing decimal numbers.
 What does a problem look like?
Example: Solve.

Answer:
What do I need to know?
When the equation contains decimals, write your answer as a decimal.
C. Solve linear equations containing fractions.
 What does a problem look like?
Examples: Solve.
1)
Answer:
2)
Answer:
3)
(
)
Answer:
 What do I need to know?
Multiply each term by the LCD of all fractions to change them all into whole
numbers.
Summary: Follow the following steps for solving equations.
1. Multiply each term on both sides by the LCD of all fractions.
2. Distribute to remove parentheses.
3. Combine like terms.
4. Use the addition property to isolate the term with the variable.
5. Use the multiplication property to isolate the variable.
6. Check your solution with the original equation.
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