Unit 2: One Variable Equations and Inequalities



Unit 2: One Variable Equations and Inequalities

Day 5 : Solving and Graphing Inequalities and Word Problems

I. Examples. Graph on a number line.

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

II. Examples. Solve and Graph on a number line.

7) [pic] 8) [pic]

WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE, .

9) [pic] 10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

III. Homework

A. Solve and Graph the following inequalities.

5) [pic] 6) [pic] 7) [pic]

8) [pic] 9) [pic] 10) [pic]

11) [pic] 12) [pic] 13) [pic]

14) [pic] 15) [pic] 16) [pic] 17) [pic]

IV. Basics: Match each inequality with its corresponding statement.

1. [pic] a. Three times a number is at most 9.

2. [pic] b. One third of a number is no more than nine.

3. [pic] c. Negative three times a number is more than nine.

4. [pic] d. Three times a number is less than nine.

5. [pic] e. Negative three times a number is at least nine.

6. [pic] f. One third of a number is greater than or equal to nine.

Write an inequality. Then solve.

7) Four times a number is greater than –48.

8) One eighth of a number is less than or equal to 3.

9) Negative twelve times a number is no more than 84.

10) Negative one sixth of a number is less than –9.

V. Examples: Assign variables, write an inequality, and solve.

1) 16 is more than 5 times a number increased by 1. Find

the largest possible value of the number.

2) Twice the sum of a number and 5 is no more than 3

times that same number increased by 11. Find the

smallest possible value of the number.

3) Carl wants to replace the five windows in the second

story bedrooms of his house. His neighbor Will is a

carpenter and he has agreed to help install them for

$250. If Carl has budgeted $1000 for the total cost,

what is the maximum amount he can spend on each

window?

4) The final grade for a class is calculated by taking 75%

of the average test score and adding to it 25% of the

score on the final exam. If all scores are out of 100

and a students has a 76 test average, what score does

the student need to make on the final exam to have a

final grade of at least 80?

5) Carmen’s scores on three math tests were 91, 95,

and 88. The fourth and final test of the grading

period is tomorrow. She needs an average (mean) of

at least 92 to receive an A for the grading period. If

Carmen wants an A in math, what must she score on

the test?

6) Find all the sets of three consecutive positive even

integers whose sum is less than 40.

VI. Homework

1) Twenty more than a number is less than twice the same

number. Find the smallest possible value of the number.

2) 9 less than a number is at most that same number

divided by 2. Find the largest possible value of the

number.

3) Jeffery has grades of 93 and 81 on the first two tests of

the quarter. Progress reports will go home after the

third test. If Jeffery does not have a A average on his progress report, he can not go to the football game

that week. Jeffery will have to make at least what grade on the third test to be allowed to go to the football

game?

4) A trucking company is hired to deliver 125 lamps for

$12 each. The company agrees to pay $45 for each

lamp that is broken during transport. If the trucking

company needs to receive at least a payment of $1365,

find the maximum number of lamps that can be broken

during transport.

5) The melting point for an element is the temperature

where the element changes from a solid to a liquid.

If C represents degrees Celsius and F represents degrees

Fahrenheit, then [pic]. Mercury is a metal

that is a liquid at room temperature. In fact, its melting

point is [pic]. Mercury is used in thermometers

because it expands evenly as it is heated. Write and

solve an inequality that can be used to find the

temperature degrees Fahrenheit for which mercury

is a solid.

6) Keith weighs 200 pounds. He wants to weigh less

than 175 points. If he can lose an average of 2 pounds

per week on a certain diet, how long should he stay

on his diet to reach his goal weight?

7) By definition, the measure of any acute angle is less

than 90 degrees. Suppose the measure of an acute

angle is [pic]. Write and solve the inequality.

8) Find all sets of two consecutive positive odd integers

whose sum is no greater than 18.

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