Algebra 1 3-1 Complete Lesson: Inequalities and Their Graphs
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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?
Problem 1 Got It?
Problem 1 Got It?
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
x > -4
3 ≤ n
Graph A
Graph B
Graph C
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.
Compare and Contrast: What are some situations you could model with x ≥ 0? How do they differ from situations you could model with x > 0?
Review Lesson 2-10: Original amounts and new amounts are paired below. Categorize each pair as an increase or decrease.
original amount: $10 ; new amount: $12
original amount: 20 in ; new amount: 18 in
original amount: 36° ; new amount: 12°
Increase
Decrease
Review Lesson 2-10: Original amounts and new amounts are paired below. Match each pair with its percent change, rounded to the nearest percent.
original amount: $10 ; new amount: $12
original amount: 20 in ; new amount: 18 in
original amount: 36° ; new amount: 12°
10% decrease
67% decrease
20% increase
Review Lesson 1-6: Find the product.
Enter only a number.
Review Lesson 1-6: Find the product.
Enter only a number, in this format: -2/17
Review Lesson 1-6: Find the quotient.
Enter only a number.
Review Lesson 1-6: Find the quotient.
Enter only a number, in this format: -17/2
Review Lesson 2-1: Solve the equation.
Enter only a number.
Review Lesson 2-1: Solve the equation.
Enter only a number, as a reduced fraction in this form: -7/8
Vocabulary Review: Write an equation using 3, 13, and k.
Use Your Vocabulary: Categorize each mathematical sentence as an equation or inequality.
17 ≥ 5
3x = 9
2x > 5
2(4) = 8
8 < 3x
Equation
Inequality
Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.
Reflection: Math Success