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Questions and Answers
What should you do when you multiply or divide by a negative number in an inequality?
What should you do when you multiply or divide by a negative number in an inequality?
Reverse the direction of the inequality symbol.
Solve the inequality x - 2 < 4.
Solve the inequality x - 2 < 4.
x < 6
What does a solid circle indicate on a graph of an inequality?
What does a solid circle indicate on a graph of an inequality?
The number is included in the solution.
Solve the inequality -3y ≤ 9.
Solve the inequality -3y ≤ 9.
In the inequality x - 4 < 1, x must be __________.
In the inequality x - 4 < 1, x must be __________.
In the inequality b - 4 ≤ -3, b must be __________.
In the inequality b - 4 ≤ -3, b must be __________.
In the inequality 6c < 24, c must be __________.
In the inequality 6c < 24, c must be __________.
In the inequality -4.2 + g ≥ 0.5, g must be __________.
In the inequality -4.2 + g ≥ 0.5, g must be __________.
In the inequality 0 ≤ -m + 6, m must be __________.
In the inequality 0 ≤ -m + 6, m must be __________.
What symbol is used to indicate that a number is not included in the solution set?
What symbol is used to indicate that a number is not included in the solution set?
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Study Notes
Inequalities Overview
- Inequalities are solved similarly to equations by applying properties of equality to maintain truth in the statement.
- Dividing or multiplying both sides of an inequality by a negative number requires reversing the direction of the inequality symbol.
Example Inequality Solutions
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For the inequality ( x - 2 < 4 ):
- Isolate ( x ) by adding 2 to both sides: ( x < 6 ).
- Graph the solution with an open circle at 6, indicating 6 is not included.
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For the inequality ( -3y \leq 9 ):
- Divide both sides by -3, reversing the inequality: ( y \geq -3 ).
- Graph the solution with a solid circle at -3, indicating -3 is included.
Graphing Techniques
- Use an open circle for inequalities with "<" or ">" symbols to indicate that the endpoint is not included in the solution.
- Use a solid circle for inequalities with "≤" or "≥" to indicate that the endpoint is included.
Practice Problems
- Solve and graph solutions for the following inequalities:
- ( x - 4 < 1 )
- ( 7 < w + 2 )
- ( 10 \leq y + 8 )
- ( 2.5a < 15 )
- ( b - 4 \leq -3 )
- ( 6c < 24 )
- ( 4t > -14 )
- ( -4.2 + g \geq 0.5 )
- ( 8 - k < 8 )
- ( \frac{3p}{5} \geq -9 )
- ( 0 \leq -m + 6 )
- ( -\frac{6}{23} < x )
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