Inequalities - practice problems
Inequalities are mathematical statements that compare two expressions using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Solving inequalities involves finding all values that make the inequality true, often resulting in a range or interval of solutions. Key concepts include understanding how multiplication or division by negative numbers reverses the inequality sign. Inequalities are used to model constraints in optimization problems, describe feasible regions in linear programming, and express ranges in real-world applications. Students learn to solve linear, quadratic, and absolute value inequalities both algebraically and graphically. Compound inequalities combine multiple conditions using "and" or "or" logic.Directions: Solve each problem carefully. Show all your work.
Number of problems found: 96
- Triangles - segments
How many triangles can be formed with segments measuring 1 2/3 mm, 3/4 mm, and 2 1/2 mm? - Negative term
Which term of the AP 24,21,18,15,.....is the first negative term? - Telephones
The cost of manufacturing x telephones by Josh Mobiles is given by C = 500 + 45x, and the revenue from selling these are given by R = 65x. How many telephones must be produced and sold in order to realize a profit? - Yoshi's
Yoshi's father gave him 200 Pokemon cards. Each week, Yoshi purchases 25 Pokemon cards to add to his collection. Which inequality can be used to find w, the number of weeks after starting his collection when Yoshi will have more than 750 Pokemon cards in - Solve 23
Solve the following inequality: 4 - ½ (2 x - 3) < 1/3 (5 - 3 x) - Sophie 2
Sophie earns $12.80 per hour babysitting. She has to repay a loan to her parents in the amount of $100. After repaying the loan, she wants to have at least enough money to buy herself a pair of sneakers costing $130.40. Write an inequality modeling the nu - Flat internet program
Under her cell phone plan, Sarah pays a flat cost of $69 per month and $4 per gigabyte. She wants to keep her bill at $83.80 per month. Write and solve an equation that can be used to determine the number of gigabytes of data Sarah can use while staying w - The sum 37
The sum of 5 and one-sixth of a number x is equal to 12 less than x plus 2/5. Find x. - A gym
The A gym offers two packages for yearly memberships. The first plan costs $50 to be a member. Then, when you visit the gum, it is $5 to get in. The second plan costs $200, but it only costs $2 to get in each time you visit. How many visits would it take - Triangles - combinations
How many different triangles with sides of whole centimetres have a perimeter of 12 cm? - Four-digit - sum
A four-digit number has a digit sum of 20. The sum of its last two digits equals the second digit increased by 5. The sum of the first and last digits equals the second digit decreased by 3. If we write the digits of this number in reverse order, the numb - Lifetime - bell curve
Laser lifetime follows a normal distribution with a mean of 7000 hours and a standard deviation of 600 hours. What is the probability that the laser will fail before 6000 hours? What is the probability that the laser will last at least 7500 hours? - Distance
If Dana increases her walking speed by 1 km/h, she will cover more than 20 km in 4 hours. If she decreases her speed by 1 km/h, she will cover no more than 20 km in 5 hours. At what speed did Dana walk? (s = v · t; s = distance, v = speed, t = time.) Solv - Real Numbers on Line
On the number line, display all real numbers greater than or equal to two and less than 5. - Inequality solution number
Which number is not a solution to the following inequality? 3 < 2 ⋅ (3x - 9) a) 6 b) 5 c) 4 d) 3 - Natural number fraction Find a natural number about which: if we subtract 2 from this number and divide the result by three, we get a fraction less than 1
- Triangle sides - natural
In triangle ABC, side a = 30 cm b = 7 cm. The length of the third side in cm is a natural number. What is the least and what is the greatest length that side c can have? - Car rental tariff
Mr. Rezek wants to rent an Opel Corsa car for one day. He can choose from two rental tariffs: Tariff 1: Daily flat rate of CZK 1,400. Tariff 2: Daily rental 360 CZK plus 4.50 CZK for each kilometer driven. For what number of kilometers driven is it more f - City baths
In the city baths, each visitor pays 100 Kč (Czech crown) for 90 minutes. With a city card, the visitor pays for the same time 50 Kč. The price of the city card is 300 Kč. Martin and Emil always go swimming together and their visit lasts exactly 90 minute - Karel grade average
Charles has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one.
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