Lesson 4 Greater Than? Develop Understanding

Jump Start

Which One Doesn’t Belong? Examine each of the models below and determine which one is different from the rest. Be prepared to justify your answer.

$x + 4$

Reason:

Learning Focus

Reason about inequalities.

Justify properties of inequalities.

Use inequality notation.

What are the properties of inequalities? Are they different from the properties of equations?

Open Up the Math: Launch, Explore, Discuss

Given a mathematical statement and two expressions, decide which of the two expressions is greater, if the expressions are equal, or if the relationship cannot be determined from the statement. Write an equation or inequality that shows your answer and explain why your answer is correct. Watch out—this gets tricky!

Example:

Statement: $x = 8$

Which is greater? $x + 5$ or $3 x + 2$

$3 x + 2$ is greater. $3 x + 2 > x + 5$ . Because if $x = 8$ , $3 x + 2 = 26$ , $x + 5 = 13$ , and $26 > 13$ .

1.

Statement: $n$ is an integer.

Which is greater? $n$ or $- n$

Try it yourself:

2.

Statement: $x > y$

Which is greater? $x + a$ or $y + a$

3.

Statement: $x > y$

Which is greater? $x - a$ or $y - a$

4.

Statement: $5 > 4$

Which is greater? $5 x$ or $4 x$

5.

Statement: $5 > 4$

Which is greater? $\frac{5}{x}$ or $\frac{4}{x}$

6.

Statement: $y < x$

Which is greater? $x - y$ or $y - x$

7.

Statement: $2 x - 3 > 7$

Which is greater? $5$ or $x$

8.

Statement: $10 - 2 x < 6$

Which is greater? $x$ or $2$

9.

Statement: $4 x \leq 0$

Which is greater? $1$ or $x$

10.

Statement: $0 < x < 10$ and $0 < y < 12$

Which is greater? $x$ or $y$

11.

Statement: $3^{n + 2} \geq 27$

Which is greater? $n$ or $1$

Ready for More?

Here is one more problem that will make you dig a little deeper. See what you can do!

Statement: $a > 0, b < 0$

Which is greater? $a b$ or $\frac{a}{b}$ ?

Takeaways

Properties of Inequalities

Addition Property:

Subtraction Property:

Multiplication Property:

Division Property:

Vocabulary

inequality
properties of inequality
Bold terms are new in this lesson.

Lesson Summary

In this lesson, we reasoned about inequalities to compare algebraic expressions. We found and justified the addition, subtraction, multiplication, and division properties of inequalities.

Retrieval

1.

Write an equation to fit with the story, and solve to answer the question.

Augustus has made a pile of $2,000$ candies, and he is giving away $25$ candies a day from this pile. When will he have $350$ candies left in this pile?

Evaluate each function for the indicated values.

2.

$g (x) = 2 x - 9$

a.

$g (2) =$

b.

$g (- 7) =$

3.

$h (x) = - 5 x + 2$

a.

$h (- 4) =$

b.

$h (6) =$

Solve each of the literal equations for the indicated variable.

4.

$R = 7 Q$ Solve for $Q$ .

5.

$2 m - 5 = y$ Solve for $m$ .