When am I ever going to use it? Your parents and grandparents want you to start  eating a healthy breakfast. The table shows the  nutritional requirements for a healthy breakfast  cereal with milk. Did you compare your favorite  cereal's nutritional values to the  healthy requirements on the table? Answer Healthy Breakfast Cereals (per serving) If you did, you found out that you  have been eating a healthy  breakfast. Now you can prove it  to your parents and  grandparents. 1. Suppose your favorite cereal has 2 grams of fat,  7 grams of protein, 3 grams of fiber and 4 grams of  sugar. Is it a healthy cereal?

Healthy Breakfast Cereals (per serving) A cereal with 3 grams of fiber just  makes it at being healthy. It needed  at least 3 grams. Answer 2. Is a cereal with 3 grams of fiber considered  healthy?

Healthy Breakfast Cereals (per serving) Answer A cereal with 5 grams of sugar is  still considered healthy but is  very close to being unhealthy. 3. Is a cereal with 5 grams of sugar considered  healthy?

Graphing and Writing Inequalities with One Variable Return to   Table of   Contents

Graphing and Writing Inequalities with One Variable Objectives Identify solutions of inequalities  with one variable. Write and graph inequalities with  one variable.

When you need to use an inequality to solve a  word problem, you may encounter one of the  phrases below.

When you need to use an inequality to solve a word  problem, you may encounter one of the phrases  below.

How are these inequalities read? 2 + 2 > 3  Two plus two is greater than 3 2 + 2 > 3  Two plus two is greater than or equal to 3 2 + 2 ≥ 4  Two plus two is greater than or equal to 4 2 + 2 < 5  Two plus two is less than 5 2 + 2 ≤ 5 Two plus two is less than or equal to 5 2 + 2 ≤ 4  Two plus two is less than or equal to 4

Writing inequalities Let's translate each statement into an inequality. words x is less than 10 translate to inequality statement 10 x < 20 is greater than or equal to y 20 > y

You try a few: 1. 14 > a 2. b ≤ 8 3. 6 < 20f 4. t + 9 ≥ 36 5. 7 + w ≤ 10 6. 19 - p ≥ 2 7. n < 12 8. s < 50 9. p > 275 1. 14 is greater than a 2. b is less than or equal to 8 3. 6 is less than the product of f and 20 4. The sum of t and 9 is greater than or equal to 36 5. 7 more than w is less than or equal to 10 6. 19 decreased by p is greater than or equal to 2 7. Fewer than 12 items 8. No more than 50 students 9. At least 275 people attended the play Answers

Do you speak math? Try to change the following expressions from  English into math. Answer 2x ≤ 6 Twice a number is at most six. Answer 2 + x ≥ 4 Two plus a number is at least four.

Three less than a number is less than three  times that number. x - 3 < 3x Answer The sum of two consecutive numbers is at  least thirteen. Answer x + (x + 1) ≥ 13 Three times a number plus one is at least ten. 3x + 1 > 10 Answer

Solution Sets A solution to an inequality is NOT a  single number. It will have more  than one value. 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 This would be read as the solution set  is all numbers greater than or equal to  negative 5.

Let's name the numbers that are solutions of the  given inequality. r > 10 Which of the following are solutions? {5, 10, 15, 20} 10 > 10 is not true So, not a solution 5 > 10 is not true So, not a solution 15 > 10 is true So, 15 is a solution 20 > 10 is true So, 20 is a solution Answer: {15, 20} are solutions of the inequality r > 10

Let's try another one. 30 ≥ 5d; {4,5,6,7,8} 30 ≥ 5d 30 ≥ 5(5) 30 ≥ 25 30 ≥ 5d 30 ≥ 5(4) 30 ≥ 20 30 ≥ 5d 30 ≥ 5(6) 30 ≥ 30 30 ≥ 5d 30 ≥ 5(7) 30 ≥ 35 30 ≥ 5d 30 ≥ 5(8) 30 ≥ 40 Answer: {4,5,6}

Graphing Inequalities with  Greater/Less Than or Equal To An open circle on a number shows that the  number is not part of the solution. It is used with "greater than" and "less than". The word equal is not included. < > A closed circle on a number shows that the  number is part of the solution. It is used with "greater than or equal to" and  "less than or equal to". < >

Remember! Open circle means that  number is not included in the  solution set and is used to  represent < or >. Closed circle means the solution  set includes that number and is  used to represent ≤ or ≥.

Graphing Inequalities Do you know where to start? How do represent the starting point? Is there a special symbol?

Graphing Inequalities Step 1: Figure out what the inequality solution  requires. For example, rewrite x is less than one  as x < 1. Step 2: Draw a circle on the number line where  the number being graphed is represented. In  this case, an open circle since it represents the  starting point for the inequality solution but is  not part of the solution. -5 5 -4 -3 -2 -1 1 2 0 3 4

x < 1 Step 3: Draw an arrow on the number line showing  all possible solutions. For numbers greater than the  variable, shade to the right of the boundary point.  For numbers less than the variable, shade to the left  of the boundary point. -5 5 -4 -3 -2 -1 1 2 0 3 4 Step 4: Draw a line, thicker than the horizontal line,  from the dot to the arrow. This represents all of the  numbers that fulfill the inequality. -5 5 -4 -3 -2 -1 1 2 0 3 4

Graphing Inequalities Step 1: Figure out what the inequality solution  requires. For example, rewrite x is greater than  or equal to one as x > 1. Step 2: Draw a circle on the number line where  the number being graphed is represented. In  this case, a closed circle since it represents the  starting point for the inequality solution and is a  part of the solution. 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

You try Graph the inequality x > 5 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Graph the inequality -3 > x 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Try these. Graph the inequalities. 1. x > 4    -5 -4 -3 -2 -1 1 2 5 0 3 4 2. x < -5 -5 -4 -3 -2 -1 1 2 5 0 3 4

Try these. State the inequality shown. 1.     -5 -4 -3 -2 -1 1 2 5 0 3 4 2.     -5 -4 -3 -2 -1 1 2 5 0 3 4

7 Would this solution set be x > 4? True False 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Remember! Closed circle means the solution set includes that number and is used to represent ≤ or ≥. Open circle means that number is not included in the solution set and is used to represent < or >.

8 -5 5 -4 -3 -2 -1 0 1 2 3 4 A x > 3 B x < 3 C x < 3 D x > 3

9 5 6 7 8 9 10 11 12 13 14 15 A 11 < x B 11 > x C 11 > x D 11 < x

10 -5 5 -4 -3 -2 -1 0 1 2 3 4 A x > -1 B x < -1 C x < -1 D x > -1

11 -5 5 -4 -3 -2 -1 0 1 2 3 4 A -4 < x B -4 > x C -4 < x D -4 > x

12 -5 5 -4 -3 -2 -1 0 1 2 3 4 A x > 0 B x < 0 C x < 0 D x > 0

A store's employees earn at least $7.50 per hour.  Define a variable and write an inequality for the  amount the employees may earn per hour. Graph  the solutions. Let e represent an employee's wages. An employee earns e at least > $7.50 7.5 7.5 0  1  2  3  4  5  6  7  8  9  10

Try this: The speed limit on a road is 55 miles per hour.  Define a variable, write an inequality and graph the  solution. Let s = speed 0 < s < 55 Answer -10 0 10 20 30 40 50 60

13 The sign shown below is posted in front of a roller coaster ride at the Wadsworth County Fairgrounds. If h represents the height of a rider  in inches, what is a correct translation of the statement on this sign? All riders MUST be at least 48 inches tall. A h < 48 B h > 48 C h ≤ 48 D h ≥ 48

Simple Inequalities  Involving Addition and Subtraction Return to   Table of   Contents

Objectives Solve one-step inequalities by  using addition. Solve one-step inequalities by  using subtraction.

Who remembers how to solve an algebraic  equation? x + 3 = 13 - 3 - 3 x = 10 Use the inverse of addition Does 10 + 3 = 13 13 = 13 Be sure to check  your answer!

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  inequalities and inverse operations.

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