Podcast
Questions and Answers
Given the inequality $3/4(12x - 8) - (x + 3) > k - 16(k/2)$, which of the following represents the solution set for $x$ when $k = 7$?
Given the inequality $3/4(12x - 8) - (x + 3) > k - 16(k/2)$, which of the following represents the solution set for $x$ when $k = 7$?
- $x < 11/8$
- $x > 11/8$ (correct)
- $x < -11/8$
- $x > -11/8$
Elaine has a $1800 budget for a party. She hires a DJ for 4 hours at $220 per hour. If the party planner costs $75 per hour, what is the maximum number of whole hours she can hire the party planner without exceeding her budget?
Elaine has a $1800 budget for a party. She hires a DJ for 4 hours at $220 per hour. If the party planner costs $75 per hour, what is the maximum number of whole hours she can hire the party planner without exceeding her budget?
- 11 hours
- 13 hours
- 10 hours
- 12 hours (correct)
Justine is buying flashlights to donate. She buys single flashlights and packs of 4. She wants to donate at least 16 flashlights. If $x$ represents the number of single flashlights and $y$ represents the number of 4-packs, which inequality represents this situation?
Justine is buying flashlights to donate. She buys single flashlights and packs of 4. She wants to donate at least 16 flashlights. If $x$ represents the number of single flashlights and $y$ represents the number of 4-packs, which inequality represents this situation?
- $x + 4y \le 16$
- $4x + y \ge 16$
- $x + 4y \ge 16$ (correct)
- $4x + y \le 16$
Given the inequality $2 - (3/4)x > -4$, which of the following intervals represents all integers that lie in the interval $[1, 17)$ and satisfy the inequality?
Given the inequality $2 - (3/4)x > -4$, which of the following intervals represents all integers that lie in the interval $[1, 17)$ and satisfy the inequality?
Which of the following represents the solution to the inequality $2(x - 5) + 4x \ge 6x + 11$?
Which of the following represents the solution to the inequality $2(x - 5) + 4x \ge 6x + 11$?
Which of the following inequalities is represented by the graph where the shaded region is below a dashed line, and the line passes through (-2,0) and (0,2)?
Which of the following inequalities is represented by the graph where the shaded region is below a dashed line, and the line passes through (-2,0) and (0,2)?
Jacob has three less dimes than nickels. The number of quarters he has is one less than twice the number of nickels. If he needs at least $5.25, and $n$ represents the number of nickels, which inequality represents the total value of his coins in dollars?
Jacob has three less dimes than nickels. The number of quarters he has is one less than twice the number of nickels. If he needs at least $5.25, and $n$ represents the number of nickels, which inequality represents the total value of his coins in dollars?
Consider the inequality $12x - 36y > 72$. Which point satisfies the inequality?
Consider the inequality $12x - 36y > 72$. Which point satisfies the inequality?
Lauren buys chocolates that are $4 each and fruit baskets that are $12 each. She wants to spend at most $60. If $c$ represents the number of chocolates and $b$ represents the number of fruit baskets, which inequality represents this situation?
Lauren buys chocolates that are $4 each and fruit baskets that are $12 each. She wants to spend at most $60. If $c$ represents the number of chocolates and $b$ represents the number of fruit baskets, which inequality represents this situation?
Given that Lauren can buy chocolates for $4 each and fruit baskets for $12 each, and she wants to spend at most $60, which of the following combinations of chocolates ($c$) and fruit baskets ($b$) could she buy?
Given that Lauren can buy chocolates for $4 each and fruit baskets for $12 each, and she wants to spend at most $60, which of the following combinations of chocolates ($c$) and fruit baskets ($b$) could she buy?
Flashcards
What is an inequality?
What is an inequality?
A statement that compares two expressions using symbols like <, >, ≤, or ≥.
What does it mean to 'solve an inequality'?
What does it mean to 'solve an inequality'?
To find all values that make the inequality true.
What is an Interval?
What is an Interval?
The set of all numbers between two given numbers, which may or may not include the endpoints.
What is the graph of an inequality?
What is the graph of an inequality?
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Why define variables when working with inequalities?
Why define variables when working with inequalities?
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What is the boundary line in an inequality graph?
What is the boundary line in an inequality graph?
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How can you algebraically check if a point is a solution to an inequality?
How can you algebraically check if a point is a solution to an inequality?
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How can you graphically check if a point is a solution to an inequality?
How can you graphically check if a point is a solution to an inequality?
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Study Notes
- The following content focuses on solving and graphing inequalities.
Solving Mixed Inequalities
- Given inequality: (3/4)(12x – 8) - (x + 3) > k − 16((k+5)/2)
Solving the inequality for k = 7
- Substitute k = 7 to yield: (3/4)(12x – 8) - (x + 3) > 7 − 16((7+5)/2)
- Then simplify and solve for x.
Finding the Smallest Even Integer
- Determine the smallest even integer that satisfies the solved inequality from the previous step.
Budget Allocation Problem
- Elaine has a budget of $1800 for a party planner and a DJ
- The DJ costs $220 per hour and the party planner $75 per hour.
- If the DJ is hired for 4 hours, the goal is to find the maximum number of whole hours for which the party planner can be hired within the budget.
Hurricane Relief Fundraiser
- Justine is purchasing flashlights to donate to charity
- She is buying single flashlights and 4-packs of flashlights.
- She wants to donate at least 16 flashlights.
Defining Variables and Inequality
- Define appropriate variables for single flashlights and 4-packs of flashlights
- Then formulate an inequality that represents wanting at least 16 flashlights.
Graphing the Inequality
- Graph the inequality for the flashlight situation on a coordinate plane
- Ensure the axes are appropriately scaled and labeled.
Minimum Amount of 4-Packs
- Determine the minimum number of 4-packs needed to buy 3 individual flashlights
- Solve algebraically.
Solving and Graphing Inequalities
- Solve the inequality 2 - (3/4)x > -4
- Graph the solution on a number line.
Finding Integers in an Interval
- Determine all integers within the interval [1, 17) that satisfy the inequality 2 - (3/4)x > -4.
Solving Inequalities
- Solve 6x ≥ 2x
- Solve 3x + 5 > 3x - 4
- Solve 2(x - 5) + 4x ≥ 6x + 11
- Solve x/7 - (2x+3)/2 > (x+1)/14 + 3
Analyzing a Given Inequality Graphically
- Given an inequality and its corresponding graph, perform the following:
- State the inequality represented by the graph.
- Select a point on the boundary line, substitute its coordinates into the inequality, and check if it satisfies the inequality.
- Algebraically determine if the point (1,5) is a solution to the inequality.
- Graphically determine if the point (-1,-6) is a solution to the inequality.
Stating an Inequality from a Graph
- Given a graph, determine the inequality it represents.
Coin Problem
- Jacob has three less dimes than nickels, and the number of quarters he has is one less than twice the number of nickels.
- He needs a minimum of $5.25 to buy a new deck of cards.
- Find the minimum amount of each coin he needs to make the purchase.
Graphing Linear Equations and Inequalities
- Graph the linear equation y + 4 = -(1/2)(x - 5).
- Graph the linear inequality 12x - 36y > 72.
Budget Problem
- Lauren is buying chocolates for $4 each and fruit baskets for $12 each, and wants to spend at most $60
- You must define the variables and the inequality
Determine if Buying Six of Each is Possible
- Check if buying 6 of each item is possible within the $60 limit, justifying algebraically.
Graphing
- Graph inequality
Analyzing a Point on the Boundary Line
- Select a point on the boundary line of the graph and explain its meaning in the context of the question.
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Description
Learn to solve mixed inequalities and determine the smallest even integer that satisfies the solution. Explore budget allocation with constraints, such as finding the maximum hours for a party planner given a DJ's hours and a total budget. Understand forming and solving inequalities from word problems.
