Algebra 1 3-1 Guided Practice: Inequalities and Their Graphs

Solve It! By law, the height of a newly constructed building in Washington D.C., can be no greater than the width of the adjacent street, plus 20 ft. Pennsylvania Avenue, shown here, is the widest street in Washington D.C. What is the maximum allowable height of a new building?

Take Note: Categorize each phrase on the left based on the inequality symbol that represents it.

is greater than
must be less than
is at most
is at least
can not be as great as
is greater than or equal to
is less than or equal to
must be more than

<
\leq
>
\geq

Problem 1 Got It?

Take Note: Define solution of an inequality.

Take Note: Which of the following numbers are solutions of the inequality below?
x\geq3
Select all that apply.

Take Note: How many solutions exist for the inequality below?
x\geq3

Problem 2 Got It? Consider the numbers -1, 0, 1, and 3. Which are soloutions of the inequality?

-1
0
1
3

Solution of the inequality
Not a solution of the inequality

Problem 2 Got It? Reasoning:
In Problem 2, how is the solution of the related equation 2x + 1 = -3 related to the solutions of the inequality 2x + 1 > -3?

Problem 3 Got It? Match the graphs with their inequalities.

c < 0
3 ≤ n
x > -4

Graph A
Graph B
Graph C

Take Note: Tag each inequality on the right with the three items from the left that describe its graph.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

5 is not a solution of the inequality
has an arrow pointing to the right
has an open dot
has a closed dot
has an arrow pointing to the left
5 is a solution of the inequality

x<5
x\leq5
x>5
x\geq5

Solve It! By law, the height of a newly constructed building in Washington D.C., can be no greater than the width of the adjacent street, plus 20 ft. Pennsylvania Avenue, shown here, is the widest street in Washington D.C. What is the maximum allowable height of a new building?

Take Note: Categorize each phrase on the left based on the inequality symbol that represents it.

Problem 1 Got It?

Problem 1 Got It?

Take Note: Define solution of an inequality.

Take Note: Which of the following numbers are solutions of the inequality below?
x\geq3
Select all that apply.

Take Note: How many solutions exist for the inequality below?
x\geq3

Problem 2 Got It? Consider the numbers -1, 0, 1, and 3. Which are soloutions of the inequality?

Problem 2 Got It? Reasoning:
In Problem 2, how is the solution of the related equation 2x + 1 = -3 related to the solutions of the inequality 2x + 1 > -3?

Problem 3 Got It? Match the graphs with their inequalities.

Take Note: Tag each inequality on the right with the three items from the left that describe its graph.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Problem 4 Got It?

Problem 4 Got It?

Problem 5 Got It? For the inequality, can the speed be all real numbers less than or equal to 8? Explain.

Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Algebra 1 3-1 Guided Practice: Inequalities and Their Graphs

Solve It! By law, the height of a newly constructed building in Washington D.C., can be no greater than the width of the adjacent street, plus 20 ft. Pennsylvania Avenue, shown here, is the widest street in Washington D.C. What is the maximum allowable height of a new building?

Take Note: Categorize each phrase on the left based on the inequality symbol that represents it.

Problem 1 Got It?

Problem 1 Got It?

Take Note: Define solution of an inequality.

Take Note: Which of the following numbers are solutions of the inequality below? x\geq3 Select all that apply.

Take Note: How many solutions exist for the inequality below? x\geq3

Problem 2 Got It? Consider the numbers -1, 0, 1, and 3. Which are soloutions of the inequality?

Problem 2 Got It? Reasoning: In Problem 2, how is the solution of the related equation 2x + 1 = -3 related to the solutions of the inequality 2x + 1 > -3?

Problem 3 Got It? Match the graphs with their inequalities.

Take Note: Tag each inequality on the right with the three items from the left that describe its graph.You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Problem 4 Got It?

Problem 4 Got It?

Problem 5 Got It? For the inequality, can the speed be all real numbers less than or equal to 8? Explain.

Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Which of the following numbers are solutions of the inequality below?
x\geq3
Select all that apply.

Take Note: How many solutions exist for the inequality below?
x\geq3

Problem 2 Got It? Reasoning:
In Problem 2, how is the solution of the related equation 2x + 1 = -3 related to the solutions of the inequality 2x + 1 > -3?

Take Note: Tag each inequality on the right with the three items from the left that describe its graph.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.