inequality

35 added to n is greater than or equal to the sum of k and 21 Take this algebraic expression in 3 parts: 35 added to n means we have a sum: n + 35 The sum of k and 21 means we add 21 to k: k +21 The phrase greater than or equal to means an inequality using this sign (>=), so we write this as...

There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more than 14 pencils. Which of the following could be the total number of pencils in all 5 cases? A) 35 B) 45 C) 65 D) 75 Determine the minimum amount of pencils (At least means greater than or equal...

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which inequality represents the number of addional games he needs to play in order to score at least 255 points for the season? Let g be the number of games Jordan plays. Total points per game is 17g...

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be? Let my current age be a. We're given: 4/5a > 3/4(a + 1) Multiply through on the right side...

A quarter of a number is greater than or equal to 38. The phrase a number means an arbitrary variable, let's call it x. A quarter of a number means 1/4, so we have: x/4 The phrase is greater than or equal to means an inequality, so we use the >= sign in relation to 38: x/4 >= 38 <-- This is...

People with a drivers license are at least 16 years old and no older than 85 years old. Set up the inequality, where p represents the people: The phrase at least means greater than or equal to. So we use the >= sign. 16 <= p The phrase no older than means less than or equal to. So we use the...

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of fish can you buy for your aquarium? Let the number of fish be f. We have the following inequality where "at most" means less than or equal to: 3.19f <= 35 Typing this inequality into our search...

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years. Let Victoria's age be v. And her neighbor's age be n. We're given: v = n + 4 v + n <=14 <-- no more than means less than or equal to Substitute Equation (1) into Inequality (2): (n + 4) + n <= 14...

The longest bridge in america is 1700 ft long. Write an inequality that describes the length of every bridge. Let the bridge length be b. Since no bridge will ever be greater than 1700 ft, we have: b <= 1700

9 is greater than x and x is greater than 3 This is a compound inequality. We write this as: 3 < x < 9

The sum of 5 and 2x is at most 27 The sum of 5 and 2x means we add 2x to 5: 5 + 2x The phrase at most means less than or equal to, so we have an inequality where 5 + 2x is less than or equal to 27 5 + 2x <= 27

50 is more than the product of 4 and w Take this algebraic expression in pieces: The product of 4 and w mean we multiply the variable w by 4: 4w The phrase is more than means an inequality using the (>) sign, where 50 is greater than 4w: 50 > 4w

3 times a number increased by 1 is between -8 and 13. Let's take this algebraic expression in 4 parts: Part 1 - The phrase a number means an arbitrary variable, let's call it x: x Part 2 - 3 times this number means we multiply x by 3: 3x Part 3 - Increased by 1 means we add 1 to 3x: 3x + 1...

the sum of 5 and y is less than or equal to -21 Take this algebraic expression in parts: The sum of 5 and y means we add y to 5 5 + y The phrase less than or equal to -21 means an inequality. We use the <= sign to relate 5 + y to -21 5 + y <= -21

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old...

8 more than twice a number is less than 6 more than the number. This is an algebraic expression, let's take it in pieces... The phrase a number means an arbitrary variable, let's call it x. 8 more than twice a number: Twice a number means multiply x by 2: 2x Then add 8: 2x + 8 6 more than...

The sum of 2 and w is less than or equal to 27. Take this algebraic expression in parts: The sum of 2 and w: 2 + w The phrase less than or equal to means an inequality, using the <= sign. 2 + w <= 27

The difference of twice a number and 6 is at most 28 This is an algebraic expression. Let's take it in parts: The phrase a number, means an arbitrary variable, let's call it x Twice this number means we multiply x by 2: 2x The difference of means subtract, so we subtract 6 to 2x: 2x - 6 Is at...

X to the 9th is less than or equal to 38: x to the 9th means 9th power: x^9 We set this less than or equal 38: x^9 <= 38

6 times a number, x, is at least 22. 6 times a number x: 6x The phrase is at least means greater than or equal to. So we have an inequality: 6x >= 22 <-- This is our algebraic expression To solve this for x, paste this into the search engine and we get: x >= 3.666667