holt mcdougal algebra 1 2-1 graphing and writing inequalities an inequality is a statement that two...
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Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs:
≤A ≤ B
A is less than or
equal to B.
<A < B
A is lessthan B.
>A > B
A is greaterthan B.
≥A ≥ B
A is greaterthan or
equal to B.
≠A ≠ B
A is notequal to B.
A solution of an inequality is any value of the variable that makes the inequality true.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Reading Math
“No more than” means “less than or equal to.”
“At least” means “greater than or equal to”.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Example 4: ApplicationRay’s dad told him not to turn on the air conditioner unless the temperature is at least 85°F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions.Let t represent the temperatures at which Ray can turn on the air conditioner.
75 80 85 9070
Turn on the AC when temperature is at least 85°F
t ≥ 85
Draw a solid circle at 85. Shade all numbers greater than 85 and draw an arrow pointing to the right.
t 85
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Solving one-step inequalities is much like solving one-step equations. To solve an inequality, you need to isolate the variable using the properties of inequality and inverse operations.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Example 1A: Using Addition and Subtraction to SolveInequalities
Solve the inequality and graph the solutions.
x + 12 < 20 x + 12 < 20
–12 –12x + 0 < 8
x < 8
Since 12 is added to x, subtract 12 from both sides to undo the addition.
–10 –8 –6 –4 –2 0 2 4 6 8 10Draw an empty circle at 8.
Shade all numbers less than 8 and draw an arrow pointing to the left.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Example 1C: Using Addition and Subtraction to SolveInequalities
Solve the inequality and graph the solutions.
0.9 ≥ n – 0.3
Since 0.3 is subtracted from n, add 0.3 to both sides to undo the subtraction.
Draw a solid circle at 1.2.
Shade all numbers less than 1.2 and draw an arrow pointing to the left.
0 1 2
+0.3 +0.31.2 ≥ n – 0
1.2 ≥ n
0.9 ≥ n – 0.3
1.2
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Example 2: Problem-Solving Application
Understand the problem11
Sami has a gift card. She has already used $14 of the total value, which was $30. Write, solve, and graph an inequality to show how much more she can spend.
The answer will be an inequality and a graph that show all the possible amounts of money that Sami can spend.
List important information:• Sami can spend up to, or at most $30.• Sami has already spent $14.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
r < 16
0 2 4 6 8 10 12 14 16 18 20
Since r is multiplied by ,
multiply both sides by the
reciprocal of .
Example 1C: Multiplying or Dividing by a Positive Number
Solve the inequality and graph the solutions.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
–50 ≥ 5q
–10 ≥ q
Since q is multiplied by 5, divide both sides by 5.
Check It Out! Example 1b
Solve the inequality and graph the solutions.
5–5 0–10–15 15
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Example 3: Application
$4.30 times number of tubes is at most $20.00.
4.30 • p ≤ 20.00
Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy?
Let p represent the number of tubes of paint that Jill can buy.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Lesson QuizSolve each inequality and graph the solutions.
1. 8x < –24 x < –3 2. –5x ≥ 30 x ≤ –6
3. x > 20 4. x ≥ 6
5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible number of shirts she can buy?0, 1, 2, 3, 4, 5, 6, or 7 shirts