Algebra 1 Inequalities Quiz

Questions and Answers

What is the definition of an inequality?

A mathematical sentence that compares expressions

What are inequality symbols?

≡

≥ (correct)

≠

≤ (correct)

What are the key terms in inequalities?

greater than, less than, more than, less than

What are the facts or characteristics of inequalities?

Describes a range of numbers, there are multiple solutions that make an inequality true. Signup and view all the answers

How do you write inequalities?

Example: A number x minus is less than or equal to fifteen; z-7≤15 Signup and view all the answers

What is the solution of inequalities?

Value that makes the inequality true. Can have more than 1 solution. Set of all solutions is called the solution set. Signup and view all the answers

What does graphing inequalities show?

Shows solution set on a number line. Signup and view all the answers

What is the addition property of inequalities?

Adding the same number to each side produces an equivalent integer. Signup and view all the answers

What are equivalent inequalities?

Inequalities that have the same solutions. Signup and view all the answers

What is the subtraction property of inequalities?

The same number on each side closed circle ≤. Signup and view all the answers

What are real world problems in the context of inequalities?

A word problem that involves mathematical equations. Signup and view all the answers

What is the multiplication or division property of inequality?

Multiply or divide each side of the inequality by the same positive number. Signup and view all the answers

What is involved in solving multi-step inequalities?

Simplify each side if necessary. Signup and view all the answers

How do you solve multi-step inequalities on both sides?

Get the variable on one side and constants on the other, and isolate the variable. Signup and view all the answers

What are inequalities with special solutions?

No solutions, infinite solutions. Signup and view all the answers

What are word problems?

Problems with words and knowing how to set up the problem. Signup and view all the answers

What is the solution for the inequality y/-6 + 7 < ?

y > -12 Signup and view all the answers

Give an example of a non-inequality.

x = 7 Signup and view all the answers

What is the solution for the inequality 2v - 4 ≥ 8?

v ≥ 6 Signup and view all the answers

What is the solution for the inequality 95 + 91 + 77 + 89 + x/5 ≥ 90?

x ≥ 98 Signup and view all the answers

Study Notes

Inequalities Overview

An inequality is a mathematical sentence comparing expressions.
Key inequality symbols include: ≥, ≤.
Inequalities describe relationships such as greater than (>) and less than (<).

Characteristics of Inequalities

They describe a range of numbers rather than a specific solution.
Multiple values can satisfy the same inequality, known as the solution set.

Writing and Solving Inequalities

Example of writing an inequality: x - 7 ≤ 15 implies x is less than or equal to 22.
Solutions to inequalities are the values that make the inequality true, sometimes resulting in more than one solution.

Graphing and Properties of Inequalities

Graphing inequalities involves displaying the solution set on a number line.
The addition property states that adding the same number to both sides maintains equivalence.
Equivalent inequalities are those that yield the same solution.

Multiplication and Division Properties

When multiplying or dividing both sides of an inequality by a positive number, the inequality remains true.
The subtraction property maintains equivalence when subtracting the same number from both sides.

Special Cases in Inequalities

Some inequalities have no solutions or infinite solutions based on their configuration.
Common word problems involve real-world scenarios that can be translated into mathematical inequalities.

Example Inequalities

Solution for y / -6 + 7 < is y > -12.
In the inequality 2v - 4 ≥ 8, the solution is v ≥ 6.
For the equation (95 + 91 + 77 + 89 + x) / 5 ≥ 90, x must be ≥ 98.

Non-Inequalities

An equation like x = 7 does not qualify as an inequality since it presents a definitive value rather than a comparative relationship.

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Test your understanding of inequalities in Algebra 1 with this quiz. Explore definitions, symbols, and key terms related to inequalities. Perfect for reinforcing your knowledge through flashcards.