Question

Solve:

Which number line is the correct
representation of the solution?
−7 < 2x + 1 < 11

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we need to isolate the variable x. We can do this by subtracting 1 from all sides of the inequality.

-7 < 2x + 1 < 11
-7 - 1 < 2x + 1 - 1 < 11 - 1
-8 < 2x < 10

Next, we can divide all sides of the inequality by 2 to isolate x.

-8/2 < 2x/2 < 10/2
-4 < x < 5

This tells us that x is greater than -4 and less than 5, but not including -4 or 5.

Therefore, the correct number line representation of the solution is:

-4--------------5

Answer 2

is -4 closed or opened?

is 5 closed or opened?

Answer 3

[AI-generated answer — Bot GPT 3.5]

-4 is open because it is not included in the solution.

5 is open because it is not included in the solution.
So both -4 and 5 are open.

Answer 4

A town's high temperature for a given month is 98°F and the low

temperature is 75°F. Which compound inequality represents the range
of temperatures for the given month?
75 ≤ t ≤ 98
75 > t < 98
75 < t < 98
t > 98 and t < 75

Answer 5

[AI-generated answer — Bot GPT 3.5]

The compound inequality that represents the range of temperatures for the given month is:

75 ≤ t ≤ 98

Answer 6

Which gr


aph belo

w bests represent the
solution set for −2x ≤ 3x + 10 ?

Answer 7

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we can begin by getting all the x terms on one side of the inequality:

-2x ≤ 3x + 10

Next, we can subtract 3x from both sides:

-2x - 3x ≤ 3x + 10 - 3x

-5x ≤ 10

Then, we divide both sides by -5. Remember that when we divide both sides of an inequality by a negative number, the inequality sign will flip:

-5x/(-5) ≥ 10/(-5)

x ≥ -2

This tells us that x is greater than or equal to -2.

Therefore, the number line below best represents the solution set for −2x ≤ 3x + 10:

------(-2)=======>

The closed circle at -2 represents that -2 is included in the solution set, and the arrow to the right indicates that x can be any value greater than -2.

Answer 8

During your class field trip, the teacher plans

at a local restaurant and has up to $180 to
spend. Which inequality describes the most
number of Combo A meals she can purchase?
9.99x ≤ 180
8.99x ≥ 180
8.99x ≤ 180
9.99x ≥ 180

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the most number of Combo A meals the teacher can purchase, we need to determine the maximum number of Combo A meals that can be bought within the budget.

Let's assume that the cost of each Combo A meal is $8.99 (the least expensive option).

To find the maximum number of Combo A meals, we divide the total budget by the cost of one Combo A meal:

x ≤ 180 ÷ 8.99

x ≤ 20.02

Thus, the inequality that describes the most number of Combo A meals the teacher can purchase is:

x ≤ 20.02

However, it's important to note that the teacher cannot purchase a fraction of a meal, so the actual feasible number of Combo A meals would be x ≤ 20.

Therefore, the correct inequality would be:

8.99x ≤ 180

Answer 10

Joanne drives a tour bus in Hollywood that can

hold up to 10 passengers. She charges each
passenger $15 dollars to ride. What is a
reasonable range for this scenario (see graph at
right)?
0,1,2,3,4,5,6,7,8,9,10
0,15,30,45,60,75,90,105,120,135,150
0 ≤ x ≤ 10
1,15,2,30,3,45,4,60,5,75,6,90

Answer 11

[AI-generated answer — Bot GPT 3.5]

A reasonable range for this scenario would be the number of passengers ranging from 0 to 10. This represents the number of passengers that Joanne's tour bus can hold. Each passenger is charged $15, so the corresponding values would be 0, 15, 30, 45, 60, 75, 90, 105, 120, 135, and 150. Thus, the reasonable range for this scenario would be:

0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150