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Example 5-7c Objective Solve inequalities

Example 5-7c Vocabulary Inequality A mathematical sentence that contains the, symbols

Example 5-7c Math Symbols <is less than >is greater than <is less than or equal to >Is greater than or equal to

Lesson 5 Contents Example 1Graph Solutions of Inequalities Example 2Graph Solutions of Inequalities Example 3Graph Solutions of Inequalities Example 4Graph Solutions of Inequalities Example 5Solve One-Step Inequalities Example 6Solve One-Step Inequalities

Example 5-1a Graph the inequality on a number line. 1/6 Write the inequality Draw an appropriate number line Put a circle on the starting number

Example 5-1a Graph the inequality on a number line. 1/6 Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “less than” 2 NOTE: The arrow is going the same direction as the sign! The open circle means that the number is not included in the solution. Answer:

Example 5-1b Graph the inequality on a number line. Answer: 1/6

Example 5-2a Graph the inequality on a number line. 2/6 Write the inequality Draw an appropriate number line Put a circle on the starting number

Example 5-2a Graph the inequality on a number line. 2/6 Since the sign is “greater than OR equal to” fill in the circle The closed circle means that the number is included in the solution. Answer: Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “greater than” -1

Example 5-2b Graph the inequality on a number line. Answer: 2/6

Example 5-3a Graph the inequality on a number line. 3/6 Write the inequality Draw an appropriate number line Put a circle on the starting number

Example 5-3a Graph the inequality on a number line. 3/6 Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “greater than” -3 NOTE: The arrow is going the same direction as the sign! The open circle means that the number is not included in the solution. Answer:

Example 5-3b Graph the inequality on a number line. Answer: 3/6

Example 5-4a Graph the inequality on a number line. 4/6 Write the inequality Draw an appropriate number line Put a circle on the starting number

Example 5-4a Graph the inequality on a number line. 4/6 Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “less than” 0 Since the sign is “less than OR equal to” fill in the circle The closed circle means that the number is included in the solution. Answer:

Example 5-4b Graph the inequality on a number line. Answer: 4/6

Example 5-5a Write the inequality. Solve Then graph the solution. Ask “what is being done to the variable ?” The variable is being subtracted by 7 Do the inverse operation on each side of the equal sign 5/6

Example 5-5a Bring down x - 7 Solve Then graph the solution. Add 7 Bring down < 2 Bring down x x – 7 x 5/6 x – x – < 2 Add 7 x – < Combine “like” terms x + 0 Bring down < x + 0 < Combine “like” terms x + 0 < 9

Example 5-5a Use the Identity Property to add x + 0 Solve Then graph the solution. Bring down < 9 x – 7 x 5/6 x – x – < 2x – < x + 0x + 0 <x + 0 < 9 x x < 9 Graph the solution Draw an appropriate number line

Example 5-5a Solve Then graph the solution. x – 7 x 5/6 x – x – < 2x – < x + 0x + 0 <x + 0 < 9 x x < 9 Put a circle on the starting number Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “less than” 9 x < 9 Answer:

Example 5-5b Answer: Solve Then graph the solution. 6/6

Example 5-6a Solve Graph the solution. 6/6 Write the inequality. Ask “what is being done to the variable ?” The variable is being multiplied by 6 Do the inverse operation on each side of the equal sign

Example 5-6a Solve Graph the solution. 1  x 6/6 Bring down 6x > 24 Using the fraction bar, divide 6x by 6 Divide 24 by 6 Combine “like” terms Bring down > 1  x > Combine “like” terms 1  x > 4 Use the Identity Property to multiply 1  x Bring down > 4

Example 5-6a 6/6 Graph the solution Draw an appropriate number line Put a circle on the starting number Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “greater than” 4

Example 5-6a 6/6 Since the sign is “greater than OR equal to” fill in the circle Answer:

Example 5-6b Solve Graph the solution. Answer: 6/6

End of Lesson 5 Assignment Lesson 4:5Inequalities All

Example 5-7a BASEBALL CARDS Jacob is buying uncirculated baseball cards online. The cards he has chosen are $6.70 each and the Web site charges a $1.50 service charge for each sale. If Jacob has no more than $35 to spend, how many cards can he buy? Let c represent the number of baseball cards Jacob can buy. Write the equation. Ask “what is being done to the variable first ?” c is being added by /7

Example 5-7b Do the inverse operation on each side 6.70c < Simplify 6.70c + 0 < c < Ask “what is being done to the variable second?” c is being multiplied by 6.70 Do the inverse operation on each side 7/7

Example 5-7b Answer: Jacob can buy no more than 5 baseball cards. Simplify 1c < 5 7/7

Example 5-7c BOWLING Danielle is going bowling. The charge for renting shoes is $1.25 and each game costs $2.25. If Danielle has no more than $8 to spend on bowling, how many games can she play? Answer: no more than 3 * 7/7