inequalities

Three times two less than a number is greater than or equal to five times the number. Find all of the numbers that satisfy the given conditions.Let n = a number. Choose the inequality that represents the given relationship. Which of the following is the solution set of the problem?

3(n - 2) 5n B

Briyana has $150, and she needs to save at least $560 for a spring break trip. If she can save $45 per week, how long will it take her to save enough money?Let w = weeks saving money. Write an inequality to describe the situation. What is the fewest number of full weeks Briyana would have to work to have enough money?

45w + 150 560 10 weeks

Serena makes $9 per hour cutting lawns. Each day, she earns about $15 in tips. If Serena made no less than $110 on Monday, which inequality represents h, the number of hours she worked on Monday?

9h + 15 is greater than or equal to 110

Which answer choice is a solution to the inequality 1.5x+3.75?

1.5

Which graph represents the solution set of the compound inequality -4 is less than or equal to 3x-1 and

A

Solve the inequality, then identify the graph of the solution. Which numbers are solutions to the inequality 2x - 1 > x + 2? Check all of the boxes that apply.

B 4,5

Identify the graph of the inequality 2(2x - 1) + 7 < 13 or -2x + 5 -10.

C

Which graph represents the solution set of the inequality

C

Which graph shows the solution set of the inequality 2.9(x+8)

D

A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?

M is less than or equal to 17

Find the student's error in solving the following inequality. Find the student's error in solving the following inequality.

The student should have switched the direction of the inequality sign to get -5> x for a final answer. The student should have added 4 to all parts (left, middle, and right) to get 6 < -3x < 9.

If x < 5 and x > c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions

The value of c could be 5 or any number greater than 5.

Identify the property used in each step of solving the inequality .

addition property multiplication property

Grayson charges $35 per hour plus a $35 administration fee for tax preparation. Ian charges $45 per hour plus a $15 administration fee. If h represents the number of hours of tax preparation, for what number of hours does Grayson charge more than Ian?

h is less than 2

Which represents the solution set of the inequality 5x-9 is less than or equal to 21

x is less than or equal to 6

Which is the solution set of the inequality 15y-9 is less than 36

y is less than 3

Which inequality has no solution?

3+4x is less than or equal to 2(1+2x)

Manuel has $600 in a savings account at the beginning of the summer. He wants to have at least $300 in the account at the end of the summer. He withdraws $28 each week for food. Which inequality represents w, the number of weeks Manuel can withdraw money while not dropping below a $300 balance?

600-28w is greater than or equal to300