BI Grade 7: Chapters 1-4 Flashcards
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Questions and Answers

What does the inequality $x > 5$ mean?

  • x is greater than 5 (correct)
  • x is not equal to 5
  • x is equal to 5
  • x is less than 5
  • Solve the inequality $x + 11 > 16$. What is x?

    x > 5

    What does the inequality $x < 7$ express?

  • x is greater than 7
  • x is less than 7 (correct)
  • x can be any real number
  • x is equal to 7
  • What is the solution to the inequality $x - 6 < 1$?

    <p>x &lt; 7</p> Signup and view all the answers

    What does $x ≤ -5$ mean?

    <p>x is less than or equal to -5</p> Signup and view all the answers

    Solve the inequality $x + 2 ≤ -3$. What is x?

    <p>x ≤ -5</p> Signup and view all the answers

    What does the inequality $x < -6$ imply?

    <p>x is less than -6</p> Signup and view all the answers

    What is the solution to the inequality $x - 1 < -7$?

    <p>x &lt; -6</p> Signup and view all the answers

    Translate and solve: What is $x$ if $x + 3 ≥ 1$?

    <p>x ≥ -2</p> Signup and view all the answers

    What does the inequality $x ≤ 6$ represent?

    <p>x is less than or equal to 6</p> Signup and view all the answers

    What is the solution to the inequality $x - 5 ≤ 1$?

    <p>x ≤ 6</p> Signup and view all the answers

    Match the inequality symbol to its definition:

    <p>&lt; = Is less than</p> <blockquote> <p>= Is greater than ≤ = Is less than or equal to ≥ = Is greater than or equal to</p> </blockquote> Signup and view all the answers

    When using < or > for inequalities, what type of circle is used in graphs?

    <p>Open circle</p> Signup and view all the answers

    When using ≤ or ≥ for inequalities, what type of circle is used in graphs?

    <p>Closed circle</p> Signup and view all the answers

    An equation has _________.

    <p>One solution</p> Signup and view all the answers

    An inequality has ________.

    <p>Infinitely many solutions</p> Signup and view all the answers

    The symbol $x < ext{#}$ means _________.

    <p>is smaller than, is less than, below...</p> Signup and view all the answers

    The symbol $x > ext{#}$ means _________.

    <p>is greater than, is more than, is larger than, above...</p> Signup and view all the answers

    The symbol $x ≤ ext{#}$ means _________.

    <p>maximum, at most, not more than, is not greater than...</p> Signup and view all the answers

    The symbol $x ≥ ext{#}$ means _________.

    <p>minimum, at least, is not less than, not smaller than...</p> Signup and view all the answers

    Write an inequality: Marcus needs to bike at least 80 miles this week. He has already biked 25 miles.

    <p>5x + 25 ≥ 80</p> Signup and view all the answers

    Solve the inequality: If Marcus has biked 25 miles already, how many miles must he bike each remaining day?

    <p>x ≥ 11</p> Signup and view all the answers

    Write an inequality: Jamal has $15.00 to spend and spends $7.50 on nachos. How much can he spend on Sour Straws?

    <p>7.5 + 1.5x ≤ 15</p> Signup and view all the answers

    Solve the inequality: How many Sour Straws can Jamal buy?

    <p>x ≤ 5</p> Signup and view all the answers

    Write an inequality: Taylor has a $30 gift card and buys a $9 picture frame.

    <p>9 + 3x ≤ 30</p> Signup and view all the answers

    Solve the inequality: What is the maximum number of journals Taylor can buy?

    <p>x ≤ 7</p> Signup and view all the answers

    Write an inequality: Liza wants more than $750 in her savings account before college.

    <p>12x + 300 &gt; 750</p> Signup and view all the answers

    Solve the inequality: How many hours must Liza work?

    <p>x &gt; 37.5</p> Signup and view all the answers

    Write an inequality: Dennis needs to sell over $175 worth of candy.

    <p>2.5x + 40 &gt; 175</p> Signup and view all the answers

    Solve the inequality: What additional bars must Dennis sell to win a prize?

    <p>x &gt; 54</p> Signup and view all the answers

    Write an inequality: The amusement park won't allow kids to ride until they are 48 inches tall.

    <p>0.5x + 42 ≥ 48</p> Signup and view all the answers

    Solve the inequality: How many months until Michael can ride?

    <p>x ≥ 12</p> Signup and view all the answers

    What should Emily read at least per week to reach her goal?

    <p>x &gt; 32.5 minutes</p> Signup and view all the answers

    Which inequality reflects Paulo's coin collection goals?

    <p>20 + 4m &gt; 50</p> Signup and view all the answers

    True or False: The statement $k + 6 ≥ 19$ is true if $k = 11$.

    <p>False</p> Signup and view all the answers

    True or False: The statement $16 < b + 8$ is true if $b = 22$.

    <p>True</p> Signup and view all the answers

    Study Notes

    Inequalities Overview

    • Inequalities contrast expressions, using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).
    • An open circle on a number line represents < or > without including the endpoint.
    • A closed circle signifies ≤ or ≥, indicating inclusion of the endpoint.

    Translating Inequality Statements

    • Translate word problems into mathematical inequalities to define constraints on variable x.
    • Common phrases to remember:
      • "at least" translates to ≥
      • "no more than" translates to ≤
      • "more than" translates to >

    Solving Inequalities

    • To solve inequalities, isolate the variable through addition, subtraction, multiplication, and division, similar to equations.
    • Be cautious when multiplying or dividing by a negative number, as it reverses the inequality sign.

    Application Examples

    • Marcus needs to bike at least 80 miles in a week, having already biked 25 miles; translate to 5x + 25 ≥ 80.
    • Jamal's budget at the concession stand shows how to write an inequality based on his total money spent with nachos and Sour Straws.

    Graphing Solutions

    • Graphing solutions to inequalities involves shading the region of solutions on a number line based on the type of inequality:
      • Open circles for < or >
      • Closed circles for ≤ or ≥

    Financial and Practical Scenarios

    • Inequalities can represent budgets, earnings, and expenses in various scenarios like car rentals, saving for purchases, or time limits.
    • Example: If Liza wants more than $750 in savings after working at $12/hour, the inequality is 12x + 300 > 750.

    Comparison and Evaluation

    • Use inequalities to compare different scenarios, such as earnings versus expenses, allowing for a decision-making tool in practical applications.
    • Tests for true or false statements by substituting values into the inequality.

    Key Inequality Forms

    • Translating common phrases into mathematical terms helps simplify problems:
      • "Three less than twice a number" translates to 2x - 3.
      • "A number increased by one is less than nine" translates to x + 1 < 9.

    Practice Problems

    • Formulating practice problems using different contexts enhances understanding. Example statements could involve decorating for a party, planning a budget, or scheduling study times.
    • Portfolio issues or investments can be represented as inequalities reflecting profit or loss margins.

    Summary of Important Values

    • Remember key numeric values that define common scenarios in inequalities, such as:
      • Minimum savings needed
      • Hourly rates for work
      • Costs for services or products

    This structured approach to understanding inequalities provides the foundational knowledge needed for solving a variety of mathematical problems in real-world contexts.

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    Description

    Test your understanding of inequalities with these flashcards covering Chapters 1-4 of the Grade 7 BI curriculum. Each card presents an inequality and its definition, helping reinforce your knowledge of mathematical concepts. Perfect for study sessions or quick reviews!

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