Question 1

Solve the inequality and graph the solution on the number line.
-
A) 
B) 
C) 
D)

Accepted Answer

The inequality can be rewritten as $x\geq -7$. This indicates that all values of $x$ that are greater than or equal to $-7$ satisfy the inequality. Graphing this on the number line, we put a closed circle at $-7$ and shade to the right to indicate all values greater than $-7$ are solutions. Choice B correctly shows a closed circle at $-7$ and a shaded line to the right. Without the inequality and its specific values provided, it is impossible to accurately determine the solution. The options provided are image filenames and do not provide any information about the inequality.

Question 2

Solve the problem.
-Greg is opening a car wash. He estimates his cost equation as C = 6000 + 0.06x and his revenue equation as R = 1.95x, where x is the number of cars washed in a six month period. Find the minimum number of cars that
Need to be washed in a six month period to make a profit.
A) 31,747 cars
B) 2175 cars
C) 318 cars
D) 3175 cars

Accepted Answer

To make a profit, revenue should be greater than cost. Therefore, we need to find the break-even point where R = C.

1.95x = 6000 + 0.06x
1.89x = 6000
x = 3174.60

Therefore, Greg needs to wash at least 3175 cars to make a profit. The closest option to this number is D, which is the correct answer. To make a profit, the revenue generated from washing cars must be greater than the cost incurred. Therefore, we need to find the point where R > C.

Setting the two equations equal to each other:

1.95x = 6000 + 0.06x

1.89x = 6000

x ≈ 3174.6

Since we cannot wash a fraction of a car, we round up to 3175 cars. Therefore, the minimum number of cars that need to be washed to make a profit is 3175.

The correct answer is D.

Question 3

Solve the inequality and graph the solution on the number line.
-
A) 
B) 
C) 
D)

Accepted Answer

A

Question 4

Solve the inequality. -a - 2 < -6 A) a < -4 B) a > -4 C) a > -8 D) a < -8

Accepted Answer

Add 2 to both sides of the inequality to isolate "a," which gives a < -4 as the solution. To solve the inequality, we need to isolate the variable "a" on one side of the inequality symbol. Adding 2 to both sides, we get:
a - 2 + 2 < -6 + 2
a < -4
Therefore, the correct choice is A, as a is less than -4.

Question 5

Solve the inequality and give the solution in interval notation.
-a - 5 < -9
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality and give the solution...

Question 6

Solve the inequality and graph the solution on the number line.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 7

Solve the inequality.
-
A) 
B) x < -6
C) x > -6
D)

Accepted Answer

The answer of Solve the inequality.
-
A) 
B) x < -6
C)...

Question 8

Solve the inequality and graph the solution on the number line.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 9

Solve the inequality. -2x + 8 < 20 A) x > 6 B) x < 8 C) x > 8 D) x < 6

Accepted Answer

Subtracting 8 from both sides gives 2x < 12. Dividing both sides by 2 gives x < 6.

Question 10

Solve the inequality and graph the solution on the number line.
-
A) 
B) 
C) 
D)

Accepted Answer

The inequality can be solved by first subtracting 4 from both sides to get 3x ≤ -1. Then, dividing by 3 results in x ≤ -1/3. This means that all values of x less than or equal to -1/3 are solutions, which can be represented on the number line with a closed circle at -1/3 and shading to the left. Among the choices, only option B represents this solution graphically.

Question 11

Solve the problem.
-Michael scored 67, 86, and 92 on three algebra tests. What must he score on the fourth test in order to have an average grade of at least 85?
A) 82
B) 95
C) 29
D) 61

Accepted Answer

To find out what Michael needs to score on the fourth test, we can set up an equation:

(67 + 86 + 92 + x)/4 ≥ 85

Simplifying this equation, we get:

(245 + x)/4 ≥ 85

Multiplying both sides by 4, we get:

245 + x ≥ 340

Subtracting 245 from both sides, we get:

x ≥ 95

Therefore, Michael must score at least 95 on the fourth test to have an average grade of at least 85. To have an average grade of at least 85, the sum of all four test scores must be at least (85 x 4) = 340. Michael's current total score is (67 + 86 + 92) = 245. Therefore, he must score at least (340 - 245) = 95 on the fourth test. So, the answer is choice (B).

Question 12

Solve the inequality and graph the solution on the number line.
-
A) 
B) 
C) 
D)

Accepted Answer

The solution to the inequality is x < -3. This means all values less than -3 are solutions, which can be graphed as an open circle at -3 with an arrow to the left representing all values less than -3. Choice B accurately represents this graph.

Question 13

Solve the inequality. -5z + 3 > 4z + 10 A) z < 7 B) z > 13 C) z > 7 D) z < 13

Accepted Answer

To solve this inequality, we want to isolate the variable (z) on one side. First, we'll subtract 4z from both sides:

5z + 3 > 4z + 10

5z - 4z + 3 > 10

Simplifying further:

z + 3 > 10

Subtracting 3 from both sides gives us the final answer:

z > 7

So the best choice is C, z > 7. 5z + 3 > 4z + 10
Rearranging the terms, we get:
z > 7
Therefore, the solution is z > 7, which corresponds to choice C.

Question 14

Solve the inequality and give the solution in interval notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality and give the solution...

Question 15

Solve the inequality.
-
A) 
B) x < 1
C) 
D) x ≤2

Accepted Answer

The answer of Solve the inequality.
-
A) 
B) x < 1
C)...

Question 16

Solve the inequality.
-
A) x < -3
B) 
C) x > -3
D)

Accepted Answer

The answer of Solve the inequality.
-
A) x < -3
B) 
C)...

Question 17

Solve the inequality and graph the solution on the number line.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 18

Solve the problem.
-Shaundra has $4.20 to make a long distance call at a pay phone.The rates listed on the phone for a long distance call are $1.70 for the first three minutes and $0.25 for each additional minute or portion of a minute. Find the
Maximum number of minutes Shaundra can stay on the line.
A) 17 minutes
B) 2 minutes
C) 10 minutes
D) 13 minutes

Accepted Answer

To find the maximum number of minutes Shaundra can stay on the line, we need to determine how many additional minutes she can afford after the first three minutes at $1.70.

Subtracting $1.70 from her total budget of $4.20, we get $2.50 remaining for additional minutes.

Dividing $2.50 by the rate of $0.25 per minute, we find that she can afford 10 additional minutes.

Adding the initial three minutes, the maximum number of minutes Shaundra can stay on the line is 13 minutes.

Therefore, the best choice is D. Shaundra has $4.20, and $1.70 of that can cover the first three minutes of the call, leaving her with $2.50. Each extra minute or portion of a minute costs $0.25. So, she can spend $2.50 on extra minutes.
Dividing $2.50 by $0.25, we get 10, so she can talk for 10 more minutes after the initial three minutes. Therefore, the maximum number of minutes Shaundra can stay on the line is 3 + 10 = 13 minutes. Hence, the correct answer is D) 13 minutes.

Question 19

Solve the inequality and give the solution in interval notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality and give the solution...

Question 20

Solve the inequality and give the solution in interval notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality and give the solution...

Quiz 10: Inequalities in One and Two Variables

Solve the inequality and graph the solution on the number line. -

Solve the problem. -Greg is opening a car wash. He estimates his cost equation as C = 6000 + 0.06x and his revenue equation as R = 1.95x, where x is the number of cars washed in a six month period. Find the minimum number of cars that Need to be washed in a six month period to make a profit.

Solve the inequality and graph the solution on the number line. -

Solve the inequality. -a - 2 < -6

Solve the inequality and give the solution in interval notation. -a - 5 < -9

Solve the inequality and graph the solution on the number line. -

Solve the inequality. -

Solve the inequality and graph the solution on the number line. -

Solve the inequality. -2x + 8 < 20

Solve the inequality and graph the solution on the number line. -

Solve the problem. -Michael scored 67, 86, and 92 on three algebra tests. What must he score on the fourth test in order to have an average grade of at least 85?

Solve the inequality and graph the solution on the number line. -

Solve the inequality. -5z + 3 > 4z + 10

Solve the inequality and give the solution in interval notation. -

Solve the inequality. -

Solve the inequality. -

Solve the inequality and graph the solution on the number line. -

Solve the inequality and give the solution in interval notation. -

Solve the inequality and give the solution in interval notation. -