W RITING AND G RAPHING S IMPLE I NEQUALITIES Lesson 8.3

A BAG OF TOMATOES WEIGHS MORE THAN 5 POUNDS. F IND THE POSSIBLE WEIGHTS ON A NUMBER LINE. Let x represent the possible weights, in pounds, of the tomatoes. Since you know the bag of tomatoes weighs more than 5 pounds, you can write the inequality. The inequality x > 5 is true for any value of x that is greater than 5. When x = 5, the inequality is since the bag of tomatoes must weigh 5 pounds. x > 5 NOT TRUE MORE THAN

S INCE THE INEQUALITY HAS AN INFINITE AMOUNT OF SOLUTIONS, YOU CAN REPRESENT THE SOLUTION ON THE NUMBER LINE AS FOLLOWS : X > 5 The number line above indicates that the inequality x > 5 is true for any value of x that is great then 5. This value can be a fraction, mixed number, decimal, or whole number. The circle indicates that the value below the circle is not a solution of the inequality. EMPTY

T HE FIGURE SHOWS A MEDICINE BOTTLE. Find the possible temperatures at which the medicine should be stored. You can write an inequality to show the medicine is to be stored below 20◦.__________ The solution can be represented on a number line as shown. w < 20

T IME TO PRACTICE ! R EPRESENT EACH INEQUALITY ON THE NUMBER LINE BELOW. h > 20 y< 10 p > 23 e < 14 m > 30

S USAN NEEDS AT LEAST 7 FEET OF RIBBON FOR HER CRAFT PROJECT. F IND THE POSSIBLE LENGTHS OF RIBBON THAT WOULD BE ENOUGH TO COMPLETE THE PROJECT. T HEN REPRESENT THE POSSIBLE LENGTHS ON A NUMBER LINE. Let p represent the length, in feet of the ribbon Susan needs. Since Susan needs at least 7 feet of ribbon, this means that 7 is also a possible value of p. You can write an inequality to show the possible lengths she needs:_________ ≥ means “is greater than or equal to.” The inequality p ≥ 7is true for any value of p that is greater than or equal to 7. p ≥ 7

S INCE THE INEQUALITY HAS AN INFINITE AMOUNT OF SOLUTIONS, YOU CAN REPRESENT THE SOLUTION ON THE NUMBER LINE AS FOLLOWS : p ≥ 7 The shaded circle indicates that the value below the circle is a solution of the inequality.

y ≤ -4

T HE SOLUTIONS CAN BE REPRESENTED ON A NUMBER LINE AS SHOWN. Y ≤ -4

T IME TO PRACTICE AGAIN ! R EPRESENT EACH INEQUALITY ON THE NUMBER LINE BELOW. q ≥ 3 d ≤ 12 k ≤ 25 m ≥ -28

a) x 10d) x ≥ M ATCH EACH INEQUALITY TO ITS GRAPH. B C A D

S OLVING I NEQUALITIES Lesson 8.3

I NEQUALITIES Just like when we solve equations, when we solve inequalities we must get the variable ! To do this we use inverse operations. Inverse means ! opposite ALONE

1) x + 5 < x < 15 2) w – 3 ≥ w ≥ 13 S OLVE AND G RAPH E ACH I NEQUALITY 3) 6x > 36 x > ) 2 p + 6 ≤ p ≤ 6 p ≤ 3 2 2