Questions and Answers
What is represented by the inequality n < -3?
What is represented by the inequality n > 10?
What is represented by the inequality n ≥ 14?
What does the inequality n ≤ 10 represent?
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What is the solution for x if x + 5 < 20?
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What is the solution for x if x - 4 > -8?
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What is the solution for x if 7x ≥ -35?
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What is the solution for x if x/8 < -48?
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What is the solution for x if x + 5 ≤ -6?
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What is the solution for x if x - 9 > -8?
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What is the solution for x if x + 15 < 12?
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What is the solution for x if x - 15 ≥ 50?
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What is the solution for x if x + 10 ≤ 75?
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What is the solution for x if -8x < 24?
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What is the solution for x if -5x > -35?
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What is the solution for x if x/6 ≥ -2?
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What is the solution for x if x/(-6) ≥ -2?
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What is the solution for x if 9x > 81?
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What is the solution for x if -7x < 42?
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What does the symbol < represent?
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What does the symbol > represent?
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What does the symbol ≤ represent?
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What does the symbol ≥ represent?
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Study Notes
One-Step Inequalities
- A number less than -3 is represented as n < -3.
- A number greater than 10 is denoted by n > 10.
- A number at least 14 can be expressed as n ≥ 14.
- Describing a number no more than 10 is done with n ≤ 10.
Solving Inequalities
- The inequality x + 5 < 20 simplifies to x < 15.
- From the inequality x - 4 > -8, it simplifies to x > -4.
- For 7x ≥ -35, dividing by 7 shows that x ≥ -5.
- The expression x/8 < -48 results in x < -6 after multiplication.
More Inequalities
- The inequality x + 5 ≤ -6 leads to x ≤ -11 when solved.
- The statement x - 9 > -8 resolves to x > 1.
- From x + 15 < 12, we conclude that x < -3.
- Solving x - 15 ≥ 50 results in x ≥ 65.
- The inequality x + 10 ≤ 75 simplifies to x ≤ 65.
Special Cases Involving Negative Coefficients
- The inequality -8x < 24 results in x > -3 after dividing both sides by -8.
- For -5x > -35, it translates to x < 7, dividing by -5 reverses the inequality.
- When dealing with x/6 ≥ -2, the solution is x ≥ -12.
- The inequality x/(-6) ≥ -2 simplifies to x ≤ 12, also reversing the inequality due to division by a negative.
- The expression 9x > 81 shows that x > 9 after division by 9.
- The inequality -7x < 42 resolves to x > -6.
Basic Symbols in Inequalities
- The symbol for less than is <.
- Greater than is represented by >.
- Less than or equal to is symbolized as ≤.
- Greater than or equal to appears as ≥.
- The phrase "no more than" corresponds to ≤.
- "No less than" is represented by ≥.
- The term "at least" uses the symbol ≥.
- "At most" indicates ≤.
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Test your understanding of one-step inequalities in this quiz. You will solve various inequalities and learn how to express them in mathematical notation. Perfect for reinforcing your knowledge in algebra concepts.