Podcast
Questions and Answers
What is the correct inequality representation for having at least 35 boys on the football team?
What is the correct inequality representation for having at least 35 boys on the football team?
The inequality $−2x + 4 > 16$ can be solved by isolating the variable x on one side.
The inequality $−2x + 4 > 16$ can be solved by isolating the variable x on one side.
True
What is the solution to the inequality $40 ≤ −3x + 10$?
What is the solution to the inequality $40 ≤ −3x + 10$?
x ≤ -10
The graph of $y ≥ 7$ includes all values of y that are ___ or greater.
The graph of $y ≥ 7$ includes all values of y that are ___ or greater.
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Match the following inequalities with their descriptions:
Match the following inequalities with their descriptions:
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When graphed, the inequality $−2x + 4 > 16$ will have a solution that is?
When graphed, the inequality $−2x + 4 > 16$ will have a solution that is?
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The equation $−2x + 4 < 16$ has a solution x < 8.
The equation $−2x + 4 < 16$ has a solution x < 8.
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The solution to the inequality $y > 7$ will be graphed with a ___ circle on the number line.
The solution to the inequality $y > 7$ will be graphed with a ___ circle on the number line.
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What is the solution to the inequality $7x - 2 \geq -16$?
What is the solution to the inequality $7x - 2 \geq -16$?
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No more than 250 students went on the field trip.
No more than 250 students went on the field trip.
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How much does Charles save per week?
How much does Charles save per week?
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If Charles wants to save at least $75, he needs to save for ___ weeks.
If Charles wants to save at least $75, he needs to save for ___ weeks.
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If 18 students rode in cars, how many filled each of the five buses if a maximum of 250 students attended?
If 18 students rode in cars, how many filled each of the five buses if a maximum of 250 students attended?
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Charles earns $15 for mowing his neighbor's yard.
Charles earns $15 for mowing his neighbor's yard.
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The inequality $-5 < m \leq 1$ indicates that m is greater than _____ and less than or equal to 1.
The inequality $-5 < m \leq 1$ indicates that m is greater than _____ and less than or equal to 1.
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Match the number with the appropriate operation in the given scenarios:
Match the number with the appropriate operation in the given scenarios:
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What is the first step in solving the inequality $20x + 40
eq -80$?
What is the first step in solving the inequality $20x + 40 eq -80$?
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The solution to the inequality $20x + 40
eq -80$ is $x > 4$.
The solution to the inequality $20x + 40 eq -80$ is $x > 4$.
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What is the final solution for $x$ in the inequality $20x + 40
eq -80$?
What is the final solution for $x$ in the inequality $20x + 40 eq -80$?
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To graph the inequality $20x + 40
eq -80$, the critical point to mark on the number line is ____.
To graph the inequality $20x + 40 eq -80$, the critical point to mark on the number line is ____.
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Match the following steps in solving the inequality with their descriptions:
Match the following steps in solving the inequality with their descriptions:
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What is the solution to the inequality $7x - 2 ≤ -9$?
What is the solution to the inequality $7x - 2 ≤ -9$?
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The solution to the inequality $2x + 3 > -60$ is $x > -31$.
The solution to the inequality $2x + 3 > -60$ is $x > -31$.
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What is the graph representation of the inequality $t ≤ -1$?
What is the graph representation of the inequality $t ≤ -1$?
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The solution to the compound inequality $w ≤ -3$ or $w > 6$ can be expressed as w is in the ______ or ______.
The solution to the compound inequality $w ≤ -3$ or $w > 6$ can be expressed as w is in the ______ or ______.
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Match each inequality with its representation:
Match each inequality with its representation:
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Which inequality symbol represents 'less than'?
Which inequality symbol represents 'less than'?
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The inequality symbol '≥' means 'greater than or equal to'.
The inequality symbol '≥' means 'greater than or equal to'.
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What is the primary difference between the symbols '>' and '≥'?
What is the primary difference between the symbols '>' and '≥'?
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In the inequality $x < 5$, the value of x must be ___ than 5.
In the inequality $x < 5$, the value of x must be ___ than 5.
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Match the following inequality symbols with their meanings:
Match the following inequality symbols with their meanings:
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Study Notes
Inequalities - Study Guide
- Graphing Inequalities: Represent inequalities on a number line. Use a closed circle for 'less than or equal to' or 'greater than or equal to' and an open circle for 'less than' or 'greater than'.
- Solving Inequalities (1-variable): Follow arithmetic principles to isolate the variable. Remember to reverse the inequality symbol when multiplying or dividing by a negative number.
- Inequality word problems: Translate words into inequalities and then solve them using the correct mathematical steps and logic.
Example Problems
-
Problem 1: Graph the inequality y ≥ 7
- Graph a closed circle at 7 on the number line and draw an arrow to the right.
-
Problem 2: Solve 40 ≤ −3x + 10
- Subtract 10 from both sides: 30 ≤ −3x
- Divide both sides by -3, and reverse the inequality sign : -10 ≥ x (or x ≤ -10)
-
Problem 3: Solve 7x - 2 ≤ -16
- Add 2 to both sides 7x ≤ -14
- Divide by 7 x ≤ -2
- Graph a closed circle at -2 and a line extending to the left.
-
Problem 4: Charles saves $5 per week. He earns extra $15 for yard work. How many weeks for at least $75?
- Let 'w' represent the number of weeks.
- Create inequality 5w + 15 ≥ 75
- Solve for w: w ≥ 12 weeks
-
Problem 5: Solve -2x + 4 > 16
- Subtract 4 from both sides: -2x > 12
- Divide by -2 and reverse the sign: x < -6
- Graph an open circle at -6 and a line extending to the left.
-
Problem 6: Write the inequality: At least 35 boys on the football team
- Let 'b' represent the number of boys. b ≥ 35
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Problem 7: Solve x ≤ −5
- Graph a closed circle at -5 and a line extending to the left.
- Problem 8: For a field trip, 18 students rode in cars. The remaining students filled 5 buses. No more than 250 students on the trip. How many students on each bus ? -Let 's' be the number of students per bus. -Create the Inequality 18 + 5s ≤ 250 -Solve for s: s ≤ 46.4 or 46 students max.
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Additional Problems (Page 2):
- Solve and graph the inequalities (problems 9-15) using the same principles. Pay attention to the 'or' and 'and' keywords in some inequality statements (e.g., problem 15).
- Solve 7x - 2 ≤ -9 (x ≤ -1)
- Graph -5 < m ≤ 1 (open circle at -5, closed circle at 1, line between)
- Solve 2(x + 3) > -60 (x > -33)
- Graph t ≤ −1 (closed circle at -1, line to the left)
- Solve 20x + 40 ≤ -80 (x≤-6)
- Graph w ≤ −3 or w > 6 (two separate number lines)
- Solve x ≥ -2
- Graph x ≥ -2 (closed circle at -2, line to the right).
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Description
This study guide covers the fundamentals of inequalities, including graphing on a number line, solving one-variable inequalities, and translating word problems into inequality statements. You'll learn crucial concepts such as using open and closed circles and properly handling inequalities during multiplication and division.
