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Properties Expressions Equations

One-Step Inequalities

Vocabulary Graphing Inequalities

Properties for $100

Name the Property shown below:

b + 0 = b

Answer

Identity Property of Addition

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Properties for $200

Name the Property shown below:

7 + (3 + C) = (7 + 3) + C

Answer

Associative Property of Addition

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Properties for $300

Name the Property shown below:

2*b = b*2

Answer

Commutative Property of Multiplication

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Properties for $400

Name the Property shown below:

5*1 = 5

Answer

Identity Property of Multiplication

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Properties for $500

Simplify the expression. Justify each step.

6x + 4(3 + 9x)

Answer

6x + 4(3 + 9x)

6x + 4*3 + 4 *9x => Distributive Property

6x + 12 + 36x => Multiplication

6x + 36x + 12 => Commutative Property of addition

(6 + 36)x + 12 => Distributive Property

42x + 12 => Addition

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Expressions and Equations for $100

Name the like terms in the following expression:

-3x + 42x – 2y + 1

Answer

-3x + 42x – 2y + 1

The like terms are -3x and 42x because they have the exact same variable.

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Expressions and Equations for $200

Simplify the following expression:

-3(5x – 4)

Answer

-3(5x – 4)

-3 * 5x + -3 * -4

-15x + 12

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Expressions and Equations for $300

Is the given number a solution to the equation?

-3x – 2 = 4; 2

Answer

-3x – 2 = 4; 2-3x – 2 = 4 where x = 2-3(2) – 2 = 4-6 – 2 = 4-8 ≠ 4 => No, 2 is not a

solution

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Expressions and Equations for $400

Simplify the following expression:

5 - 3(-2x + 4)

Answer

Back

5 – 3(-2x + 4)

5 + (-3)(-2x) + (-3)(4)

5 + 6x – 12

6x + 5 – 12

6x - 7

Expressions and Equations for $500

The Ramirez family has two children. The sum of their ages is 11. The product of their ages is 24. How old are the children?

Answer

Make a table!

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Age 1 Age 2 Sum Product

6 5 11 30

7 4 11 28

8 3 11 24

Vocabulary for $100

Define: Integers

Answer

Integers – All positive and negative whole numbers

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Vocabulary for $200

Define: Term

Answer

Term – Part of an expression or series separated by + or – signs, or the parts of a sequence separated by commas

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Vocabulary for $300

Define: Deductive Reasoning

Answer

Deductive Reasoning – Reasoning in which solutions are drawn from logically given facts.

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Vocabulary for $400

Define: Inequality

Answer

Inequality – A mathematical sentence that contains >, <, ≤, ≥, or ≠

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Vocabulary for $500

Define: Solution of an Inequality

Answer

Solution of an Inequality – Any number that makes the inequality true.

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Graphing Inequalities for $100

Graph the inequality shown below:

x > -4

Answer

Back

X > -4

Graphing Inequalities for $200

Write an inequality for the graph shown below:

Answer

Back

X ≤ 3

Graphing Inequalities for $300

Graph the inequality shown below:

-7 < x

Answer

Back

-7 < x

Graphing Inequalities for $400

Graph the inequality shown below:

0 ≤ x < 4

Answer

Back

0 ≤ x < 4

Graphing Inequalities for $500

Graph the inequality shown below. Check your answer:

x < -5 or x ≥ 2

Answer

Back

x < -5 or x ≥ 2

Let x = -7 Let x = -4 Let x = 5

-7 < -5 =>True -4 < - 5 => NOT True 5 < -5 => NOT True

-7 ≥ 2 =>NOT True -4 ≥ 2 => NOT True 5 ≥ 2 => True

One-Step Inequalities for $100

Solve for x:

X + 2 < 1

Answer

X + 2 < 1 -2 -2X < -1

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One-Step Inequalities for $200

Solve for x:

x/(-5) > 7

Answer

x/(-5) > 7

x/(-5) * (-5) > 7 * (-5)

X < -35

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One-Step Inequalities for $300

Solve for x:

4x ≥ -36

Answer

4x ≥ -36

(4x)/(4) ≥ (-36)/(4)

x ≥ -9

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One-Step Inequalities for $400

Write the following inequality in words:

x + 5 ≥ 7

Answer

Back

x + 5 ≥ 7

Five more than a number, x, is greater than or equal to 7

One-Step Inequalities for $500

Write an Inequality to model the following situation:

Mr. Sam spent at least 4 hours making this game

Answer

Back

Let t = the time Mr. Sam spent making this game

Then,

t ≥ 4 hours