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Unit 4: Coordinating Algebra ya
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Terms in this set (67)
Step 1: -10 + 8x < 6x - 4
Step 2: -10 < -2x - 4
Step 3: -6 < -2x
Step 4: ________
What is the final step in solving the inequality -2(5 - 4x) < 6x - 4?
x < 3
What value of x is in the solution set of 9(2x + 1) < 9x - 18?
-1
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
B
What value of x is in the solution set of 2x - 3 > 11 - 5x?
Not 2
What value of x is in the solution set of 2(3x - 1) ≥ 4x - 6?
-1
Which number line represents the solution set for the inequality -4(x + 3) ≤ -2 - 2x?
A
Which is a correct first step in solving 5 - 2x < 8x - 3?
5 < 10x - 3
Which number line represents the solution set for the inequality 2x - 6 ≥ 6(x - 2) + 8?
Not D
What value of x is in the solution set of -5x - 15 > 10 + 20x?
1
Which are correct representations of the inequality 6x ≥ 3 + 4(2x - 1)? Check all that apply.
Not
2
3
Solve the inequality.
2(4 + 2x) ≥ 5x + 5?
x ≤
3
What value of x is in the solution set of 3(x - 4) ≥ 5x + 2?
Not 5
Which number line represents the solution set for the inequality -1/4x ≥ 4?
B
Step 1: Subtract 3 from both sides of the inequality.
Step 2: __________
Step 3: Divide both sides of the inequality by the coefficient of x.
What is the missing step in solving the inequality 5 - 8x < 2x + 3?
Add 8x to both sides of the inequality.
Which is a correct first step in solving the inequality -4(2x - 1) > 5 - 3x?
Distribute -4 to get -8x + 4 > 5 - 3x.
Solve the inequality.
2(4x - 3) ≥ -3(3x) + 5x?
x ≥ 0.5
What is a correct first step in solving the inequality -4(3 - 5x)≥ -6x + 9?
-12 + 20x ≥ -6x + 9
The inequality graphed below represents the ages, a, of players on a baseball team.
Which inequality represents the same ages?
12 ≤ a < 18
Which compound inequality is represented by the graph?
-3 ≤ x < 1
A chef knows that ground beef used for hamburger is safe to eat once it reaches 160 degrees Fahrenheit. For optimized taste and safety, he will not allow a hamburger cooked to a temperature under 160 degrees or over 170 degrees to be served. Which graph represents the conditions under which the chef will not allow the hamburger to be served?
A
Which graph represents the compound inequality?
-3 < n < 1
D
The weight of a box of cereal can vary by of an ounce and still be sold as a full box. Each box is supposed to contain 18 ounces of cereal. Which graph represents the possible weights of boxes that are overfilled or underfilled?
B
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9 hours (h >9). How can these inequalities be written as one statement?
h < 7 or h > 9
Which scenario can be modeled using the graph below?
A temperature range is within 5 degrees of 60 degrees Fahrenheit.
Which graph represents the compound inequality?
h ≥ -5 and h < 2
B
To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?
A
Which situation could be represented by the graph?
Not Students in the children's choir are at least 8 years old but no more than 11 years old.
Which graph represents the solution to the compound inequality?
-6 < 3x - 12 ≤ 9
Not A
Phyllis solved the compound inequality 16 < 2(3x - 1) < 28. She began by first breaking the inequality into two separate inequalities, then she correctly solved each for x.
16 < 2(3x - 1) and 2(3x - 1) < 28
3 < x x < 5
Which graph represents her solution?
A
Which values are in the solution set of the compound inequality? Check all that apply.
4(x + 3) ≤ 0 or x + 1 > 3
Not
-3
8
The cost of one pound of bananas is greater than $0.41 and less than $0.50. Sarah pays $3.40 for x pounds of bananas. Which inequality represents the range of possible pounds purchased?
Not 0.41 < 3.40x < 0.50
Ava solved the compound inequality + 7 < -1 or 2x - 1 ≥ 9 for all possible values of x. She determines that the two inequalities below create the solution set for the compound inequality.
x < -32 or x ≥ 5
Which graph represents the solution set?
B
Solve for x.
0 ≤ 3x - 6 ≤ 18
2 ≤ x ≤ 8
Which is the best interpretation of the solution set for the compound inequality?
3(2x + 1) > 21 or 4x + 3 < 3x + 7
Not
3 < x < 4
Which compound inequality has no solution?
Not
x ≤ -1 and 5x ≤ 5
Mrs. Sawyer estimates that a quiz will take students no fewer than 11 minutes but no more than 41 minutes to complete. She allots 1 minute for passing out the papers and instructions and then students will complete a 20-question quiz. Which compound inequality represents x, the average amount of time a student spends on each question?
Not
1 + 20x ≥ 11 or 1 + 20x ≤ 41
Which graph represents the solution set of the compound inequality below?
x + 3 < (4x - 12) < 20
Not C
The solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution?
(0,2)
Which description of the graph of the linear equality y ≥ 7x - 4 is correct?
The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line
Which linear inequality is represented by the graph?
y > 3x + 2
Which linear inequality is represented by the graph?
y ≥ 1/3x − 1
Which linear inequality is represented by the graph?
y ≤ 1/2x + 2
Which linear inequality is represented by the graph?
y ≤ 1/3x - 4
Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply.
(-3, -2)
(-1, -2)
(1, -2)
(1, 2)
Which is the graph of the linear inequality y < 3x + 1?
D
Which linear inequality is represented by the graph?
y ≤ 1/3x - 1.3
Which is the graph of the linear inequality 2x - 3y < 12?
C
Which shows the graph of the solution set of y > -1/2x - 3?
B
Which shows the graph of the solution set of 2x + y < 4?
C
Last year, Jess saw x dramas and y comedies at the movie theater. If she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?
Not x + y < 8
On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"?
Not
4x + 8y ≤ 50
Hamburgers cost $2.50 and cheeseburgers cost $3.50 at a snack bar. Ben has sold no more than $30 worth of hamburgers and cheeseburgers in the first hour of business. Let x represent the number of hamburgers and y represent the number of cheeseburgers. The inequality 2.50x + 3.50y ≤ 30 represents the food sales in the first hour.
If Ben has sold 4 cheeseburgers, what is the maximum value of hamburgers Ben could have sold?
Ben could have sold no more than ____ hamburgers.
6
A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Which inequality represents the possible ways Nina can eat 12 or more grams of protein, if x is the number of cheese squares that she eats and y is the number of turkey slices that she eats?
12 ≤ 2x + 3y
Mr. Ishimoto ordered x new math books and y new workbooks for his class. The total weight of the box of books cannot be more than 50 pounds. If each math book weighs 3.2 pounds and each workbook weighs 0.8 pounds, which inequality represents the maximum number of each type of book that can be shipped in a single box?
3.2x + 0.8y ≤ 50
At lunch, Kira eats either a burrito containing 490 milligrams of sodium or a peanut butter sandwich containing 700 milligrams of sodium. Her doctor told her to reduce her sodium to no more than 4,000 milligrams per week. Which inequality represents x, the number of microwave burritos, and y, the number of peanut butter sandwiches, she can eat each week?
490x + 700y ≤ 4000
Which shows the graph of the solution set of 3y - 2x > -18?
D
Which shows the graph of the solution set of y < -4x + 3?
D
Which is true about the solution to the system of inequalities shown?
y < 1/3x - 1
y < 1/3x - 3
All values that satisfy y < 1/3x - 3 are solutions.
Which ordered pair makes both inequalities true?
y < 3x - 1
y > -x + 4
Not (2,1)
Which ordered pairs are in the solution set of the system of linear inequalities?
y > -1/2x
y < 1/2x + 1
(5, -2), (3, 1), (4, 2)
Which ordered pair makes both inequalities true?
y > -3x + 3
y > 2x - 2
(2,2)
Which system of linear inequalities is represented by the graph?
Not
y > x + 2 and x + 2y < 4
Which number completes the system of linear inequalities represented by the graph?
y > 2x - 2 and x + 4y >
-12
Which ordered pairs make both inequalities true? Check all that apply.
y < 5x + 2
y > 1/2x + 1
Not
(0, 2)
(2, 2)
Which system of linear inequalities is represented by the graph?
y > x - 2 and y < x + 1
Which graph shows the solution to the system of linear inequalities?
y < 2x - 5
y > -3x + 1
B
Which system of linear inequalities is represented by the graph?
y > 2/3x + 3 and y < -1/3x + 2
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Verified questions
ALGEBRA
A regulation NFL playing field (including the end zones) of length x and width y has a perimeter of 346 2/3 or 1040/3 yards.Draw a rectangle that gives a visual representation of the problem. Use the specified variables to label the sides of the rectangle.
ALGEBRA
Paul bought a student discount card for the bus. The card cost $7 and allows him to buy daily bus passes for$1.50. After one month, Paul spent $29.50. How many daily bus passes did Paul buy?
ALGEBRA
Heidi tries to qualify for a gymnastics team. Qualifying is based on the average of six event scores. Heidi knows she needs at least a 7.5 average in the six events to make the team. Her scores for the first five events are 6.4, 8.0, 8.1, 6.5, and 8.2. a. What is Heidi's mean event score for the five events? What is her median score? b. Suppose Heidi scores a 7.6 in the final event. Will she make the team? Show your steps. c. Make another guess about the minimum score Heidi needs to make the team. Check your guess. Keep track of your steps. d. Use the guess-check-generalize method to find an equation for the minimum score Heidi needs to make the team. e. Solve your equation.
PRECALCULUS
If a variable z varies as the product of the variables x and y, we say z varies jointly as x and y, and we write $z=k\cdot x \cdot y$, where k is the constant of variation. Write a sentence that expresses the relationship in each of the following formulas, using the language of joint variation. $F=G\cdot m_1\cdot m_2/r^2$, where F is the force of gravity acting on objects of masses $m_1$ and $m_2$ with a distance r between their centers and G is the universal gravitational constant.
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