BI Grade 7: Chapters 1-4 Flashcards

Podcast

Play an AI-generated podcast conversation about this lesson

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 $x - 6 < 1$?

x < 7 Signup and view all the answers

What does $x ≤ -5$ mean?

x is less than or equal to -5 Signup and view all the answers

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

x ≤ -5 Signup and view all the answers

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

x is less than -6 Signup and view all the answers

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

x < -6 Signup and view all the answers

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

x ≥ -2 Signup and view all the answers

What does the inequality $x ≤ 6$ represent?

x is less than or equal to 6 Signup and view all the answers

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

x ≤ 6 Signup and view all the answers

Match the inequality symbol to its definition:

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

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

Open circle Signup and view all the answers

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

Closed circle Signup and view all the answers

An equation has _________.

One solution Signup and view all the answers

An inequality has ________.

Infinitely many solutions Signup and view all the answers

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

is smaller than, is less than, below... Signup and view all the answers

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

is greater than, is more than, is larger than, above... Signup and view all the answers

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

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

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

minimum, at least, is not less than, not smaller than... 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.

5x + 25 ≥ 80 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?

x ≥ 11 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?

7.5 + 1.5x ≤ 15 Signup and view all the answers

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

x ≤ 5 Signup and view all the answers

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

9 + 3x ≤ 30 Signup and view all the answers

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

x ≤ 7 Signup and view all the answers

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

12x + 300 > 750 Signup and view all the answers

Solve the inequality: How many hours must Liza work?

x > 37.5 Signup and view all the answers

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

2.5x + 40 > 175 Signup and view all the answers

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

x > 54 Signup and view all the answers

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

0.5x + 42 ≥ 48 Signup and view all the answers

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

x ≥ 12 Signup and view all the answers

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

x > 32.5 minutes Signup and view all the answers

Which inequality reflects Paulo's coin collection goals?

20 + 4m > 50 Signup and view all the answers

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

False Signup and view all the answers

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

True 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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

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!