inequality

A number n is no less than 2 and no more than 49. This is a compound inequality. Let's break it into parts. Step 1: No more than 49 means 49 or less. Or, less than or equal to 49 <= 49 Step 2: no less than 2 means 2 or greater. Or, greater than or equal to 2 >=2 Writing this in terms of the...

You have $10.00 to spend on tacos. Each taco costs $0.50. Write and solve an inequality that explains how many tacos you can buy. Let's start with t as the number of tacos. We know that cost = price * quantity, so we have the following inequality for our taco spend: 0.5t <= 10 Divide each...

The shortest person in a class is 55 inches tall and tallest person in that class is 75 inches tall. write an absolute value equation that requires the minimum and maximum height. Use X to represent heights. We write our inequality as: 55 <= X <= 75

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An average sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement? Let a be the number of apples required. The phrase at least...

An Amazon delivery package receives a bonus if he delivers a package to a costumer in 20 minutes plus or minus 5 minutes. Which inequality or equation represents the drivers allotted time (x) to receive a bonus 20 plus 5 minutes = 25 minutes 20 minus 5 minutes = 15 minutes So we have the...

7 times a positive number n is decreased by 3, it is less than 25 7 times a positive number n: 7n Decreased by 3: 7n - 3 The phrase it is less than means an inequality. So we relate 7n - 3 less than 25 using the < sign to get our algebraic expression of: 7n - 3 < 25

9 subtracted from the product of 3 and a number is greater than or equal to 16 The phrase a number means an arbitrary variable, let's call it x The product of 3 and a number means we multiply 3 times x: 3x 9 subtracted from the product: 3x - 9 The phrase is greater than or equal to means an...

A carnival charges a $15 admission price. Each game at the carnival costs $4. How many games would a person have to play to spend at least $40? Let g be the number of games. The Spend function S(g) is: S(g) = Cost per game * number of games + admission price S(g) = 4g + 15 The problem asks for...

X is the speed limit is a maximum 65 mph A maximum of means less than or equal to. Or, no more than. So we have the inequality: X <= 65

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage? Let the number of inches be i. Remember 12 inches to a foot, so we have 2 feet = 12*2 = 24 inches...

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money from her account and still have money left? Let w be the number of weeks. We have the following equation for the Balance after w weeks: B(w) = 250 - 25w we subtract for withdrawals The ability to...

2/3 of a number 17 is at least 29 The phrase a number means an arbitrary variable, let's call it x: x 2/3 of a number means we multiply x by 2/3: 2x/3 The phrase is at least also means greater than or equal to, so we set up the inequality: 2x/3 >= 29

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the elevator? (Use "p" to represent the number of people) Maximum means less than or equal to. We have the inequality: 150p <= 3000 To solve this inequality for p, we type it in our search engine and we...

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is the better deal Let the number of days be d. We have the inequality below where we show when the day to day cost is greater than the monthly pass: 1.5d > 24 To solve this inequality for d, we...

6 diminished by twice x is at most 8 Twice x means we multiply x by 2: 2x 6 diminished by twice x means we subtract 2x from 6: 6 - 2x The phrase is at most is an inequality using the sign <=, so we have: 6 - 2x <= 8

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51 Let JP's age be j. Let Reyna's age be r. We're given two expressions: w = 2r r + w <= 51. (Does not exceed means less than or equal to) We substitute (1) into (2) for w to get the inequality: r + 2r <= 51 To solve...

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represents the number x of cups of coffee you must purchase for the monthly card to be a better deal? Let c be the number of cups. We want to know how many cups (x) where: 1.75x > 25 Using our...

the difference between A and B is no less than 30. The difference between a and b: a - b The phrase no less than means an inequality. You can also say this as greater than or equal to. a - b >= 30

the average, a, is at least 85 At least is an inequality. It also means greater than or equal to, so we have: a >= 85

harley had $500 in his bank account at the beginning of the year. he spends $20 each week on food, clothing, and movie tickets. he wants to have more than $100 at the end of summer to make sure he has enough to purchase some new shoes before school starts. how many weeks, w, can harley withdraw...