inequality

absolute value of x is less than or equal to 4 Absolute value of x: |x| Set up an inequality where this is less than or equal to 4: |x| <= 4 <-- This is our algebraic expression To solve this, we have the following compound inequality: -4 < x < 4

the difference of twice a number and 8 is at most -30. The phrase a number means an arbitrary variable, let's call it x. Twice this number means we multiply by 2, so we have 2x. We take the difference of 2x and 8, meaning we subtract 8: 2x - 8 Finally, the phrase at most means an inequality...

A bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like to keep its daily costs at or below $500 per day. Which inequality shows the maximum number of pastries, p, that can be baked each day. Set up the cost function C(p), where p is the number of...

The difference of twice a number and 4 is at least -27. The phrase a number means an arbitrary variable, let's call it x. x Twice a number means multiply the number by 2 2x and 4 means we add 4 to our expression: 2x + 4 Is at least means an inequality. In this case, it's greater than or...

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minute of use. The least she has been charged in a month is $86.04 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your...

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the rest of the money to buy shirts. Find the inequality. Let j be the number of jeans. Let s be the number of shirts. We are given: Mom told you to buy one pair of jeans. So we have $80 to start...

Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Chang wants the total calorie count from the french...

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260 person-hours per week. Tom has one part-time employeewho works 20 hours per week. Each full-time employee works 40 hours per week. Write an inequality to determine n, the number...

Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he must score at least 660 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests, n, in order to get an A. We want to know n, such that 556...

The cost to rent a construction crane is 450 per day plus 150 per hour. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed 1650 per day? Set up the cost function where h is the number of hours: C(h) = 150h + 450 We want C(h) <= 1650: 150h +...

The price of a baseball glove is no more than $38.95. Let p be the price of the baseball glove. The phrase "no more than" means less than or equal to. Our inequality is: p <= $38.95

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $75. A season ski pass costs $350. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the...

Your brother has $2000 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to find how much he can spend for everything else. Let x be the amount your brother can spend. Subtracting the cost of the plane ticket from savings, we have: x <= 2000 - 637 x <= 1,363

Four more then double a number is greater than 2 Double a number: A number implies an arbitrary variable, let's call it "x". Double means multiply this by 2 2x Four more than this: 2x + 4 Now, we set this expression as an inequality greater than 2 2x + 4 > 2

The value of 3 times the quantity of 4 + x is greater than 6 less than x. 3 times the quantity 4 + x 3(4 + x) 6 less than x x - 6 3 times the quantity 4 + x is greater than x - 6 3(4 + x) > x - 6

|(x-7)/5|<=4 Set up two equations: (x-7)/5 <= 4 (x-7)/5 > -4 Cross Multiply (1): x - 7 <= 20 Add 7 to each side: x <= 27 Cross Multiply (2): x - 7 > -20 Add 7 to each side: x > -13

Mr. Smith wants to spend less than $125 at a zoo. A ticket cost $7 he is taking 2 kids with him. Use p to represent the other money he can spend there. 2 kids and Mr. Smith = 3 people. Total Ticket Cost is 3 people * 7 per ticket = 21 If he has 125 to spend, we have the following inequality...

2x^2+4x < 3x+6 Subtract 3x from both sides: 2x^2 + x < 6 Subtract 6 from both sides 2x^2 + x - 6 < 0 Using our quadratic calculator, we get: x < 1.5 and x < -2 When we take the intersection of these, it's x < 1.5

Yolanda runs each lap in 7 minutes. She will run less than 35 minutes today. What are the possible numbers of laps she will run today? 7 minutes per lap must be less than 35 minutes. Let l be the number of laps 7l < 35 Divide each side by 7 l < 5

Translate to an inequality. The cost is smaller than $94,000. Let the cost be c. We have: c<94,000