inequality

Five less than a number is at least -7 and at most 7. A number signifies an arbitrary variable, let's call it x. Five less than a number: x - 5 Is at least -7 means greater than or equal to and at most 7 means less than or equal to, so we have a joint inequality: -7 <= x - 5 <= 7

The sum of a number b and 3 is greater than 4 and no more than 16 The sum of a number b and 3: b + 3 Greater than 4 and no more than 16 means we have a combo inequality: Greater than 4 means we use a > sign No more than 16 means less than or equal to, so <= 4 < b + 3 <= 16

Translate the sentence into an inequality. Twice y is less than 21. Twice y 2y Is less than 21 means we have an inequality: 2y < 21

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to...

4 times x plus 2 is at most 10 4 times x 4x Plus 2 4x + 2 At most means less than or equal to, so we have: 4x + 2 <= 10

The difference of twice a number and 9 is less than 22 The phrase a number, means an arbitrary variable, let's call it x. x Twice a number 2x The difference of twice a number and 9 2x - 9 Is less than 22 2x - 9 < 22

The product of x and 7 is not greater than 21 The product of x and 7: 7x Is not greater than means less than or equal to, so we have our algebraic expression: 7x <= 21 If you want to solve this inequality and interval notation, use our calculator.

7 less than -2 times a number x is greater than or equal to 41 -2 times a number x -2x 7 less than this -2x - 7 Now we set this expressions greater than or equal to 41 -2x - 7 >= 41

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Which inequality models this situation? Since dimes are worth $0.10 and quarters are worth $0.25, we have: 0.10d + 0.25q < 14.75

M decreased by the sum of 13 and the number P is less than 12 The sum of 13 and the number P 13 + P M decreased by the sum of 13 and the number P M - (13 + P) Less than 12 means we set this entire expression less than 12 as an inequality M - (13 + P) < 12

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? Each ride will cost 1.50 + 0.8x where x is the number of miles per trip. This expression...

Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10? Let n be the number of notebooks you can purchase. We have the following inequality: 1.39n <= 10 Divide each side by 1.39 n <= 7.194 We want whole notebooks, we cannot buy fractions of...

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? Set up the travel cost equation where m is the number of miles: C(m) = 0.8m + 1.50 If...

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Which inequality models this situation? Let d be the number of dimes and q be the number of quarters 0.1d + 0.25q < 14.75

The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many students can go on the field trip? Set up the inequality where s is the number of students: C(s) = 220 + 7s We want C(s) <= 500, since at most means no more than 220 + 7s <= 500 Using our...

13 more than x is greater than 14 13 more than x x + 13 Is greater than 14 x + 13 > 14

Kelsey wants to buy a new video game. He has a $50 gift card and wants to spend less than $20 of his own money. Which of the following amounts would Kelsey be willing to spend on a video game? Let x be the amount Kelsey will spend on a video game above 50. He will spend up to, but less than...

Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible numbers of additional minutes she will run? Set up our inequality. If she ran 22 minutes, we need to find an expression to find out the remaining minutes x + 22 < 36 Subtract 22 from each side: x...

x is smaller than 9 and greater than 4 Written as: 4 < x < 9 To display the interval notation, use our interval notation calculator.

-2 <= x +4 < 9 Subtract 4 from each piece: -2 - 4 <= x < 5 Simplify: -6 <= x < 5 To find the interval notation, we set up our notation: The left side has a solid bracket, since we have an equal sign: The right side has an open parentheses, since we have no equal sign [-6, 5)