Question 1

Solve the inequality  . Write the solution in set-builder notation.

Accepted Answer

The answer of Solve the inequality  . Write the...

Question 2

Solve the inequality  . Write the solution in set-builder notation.

Accepted Answer

The answer of Solve the inequality  . Write the...

Question 3

Solve the inequality  . Write the solution in interval notation.

Accepted Answer

The answer of Solve the inequality  . Write the...

Question 4

Graph the solution set for the inequality  .

Accepted Answer

The answer of Graph the solution set for the inequality...

Question 5

Graph the solution set for the inequality  .

Accepted Answer

The answer of Graph the solution set for the inequality...

Question 6

Solve the inequality  . Write the solution in interval notation.

Accepted Answer

To solve the inequality, we need to isolate the variable e by dividing both sides by 7. We get e > -3. We write this in interval notation as (-3, infinity). The correct option is C.

Question 7

Graph the solution set for the inequality  .

Accepted Answer

The answer of Graph the solution set for the inequality...

Question 8

Graph the solution set for the inequality  .

Accepted Answer

The inequality is equivalent to $|x+3|<|x-1|$. We can break it up into cases: Case 1: If $x \geq 1$, then $|x+3|=x+3$ and $|x-1|=x-1$, so we have $x+3-1$, which is satisfied by this case. Case 3: If $x < -3$, then $|x+3|=-(x+3)$ and $|x-1|=-(x-1)$, so we have $-(x+3)1$, which is not satisfied by this case. Therefore, the solution set is $-3 \leq x < -1$ or $x>1$, which is represented by choice (B) on the number line.

Question 9

At 10 A.M. a plane leaves Boston, Massachusetts, for Seattle, Washington, a distance of 3000 mi. One hour later a plane leaves Seattle for Boston. Both planes are traveling at a speed of 400 mph. How many hours after the plane leaves Seattle will the planes pass each other?

Accepted Answer

The plane leaving Boston will have a one-hour head start, so we only need to consider how long it takes the two planes to cover the remaining distance between them. The combined speed of the two planes is 800 mph (400 mph from each plane), so the amount of time it takes for them to cover the remaining 2700 miles is:

time = distance / speed
time = 2700 / 800
time = 3.375 hours

However, we need to add the one-hour head start from Boston, so the total time is:

total time = 3.375 + 1
total time = 4.375 hours

Rounding to the nearest quarter hour gives us a final answer of 3.25 hours, or choice D.

Question 10

Solve the inequality  . Write the solution in set-builder notation.

Accepted Answer

The answer of Solve the inequality  . Write the...

Question 11

Graph the solution set for the inequality  .

Accepted Answer

The inequality 11eb69da_9f01_e354_af94_85e1748d27ea_TB8311_11 can be rewritten as y > 2x - 5 by distributing the -2 and adding 5 to both sides. The solution set for this inequality is all the points graphed above the line y = 2x - 5. The correct graph is shown in choice B.

Question 12

A 565-mile, 5 hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. For the remainder of the trip, the average speed was 125 mph. How long did the plane fly at 105 mph?

Accepted Answer

Let x be the time flown at 105 mph. Then, the time flown at 125 mph is (5-x) hours.
Using the formula: distance = speed x time, we can write:
105x + 125(5-x) = 565
Solving for x, we get:
x = 3
Therefore, the plane flew for 3 hours at 105 mph. Thus, the answer is choice C.

Question 13

Solve the inequality  . Write the solution in interval notation.

Accepted Answer

The answer of Solve the inequality  . Write the...

Question 14

Solve the inequality  . Write the solution in set-builder notation.

Accepted Answer

The answer of Solve the inequality  . Write the...

Question 15

Solve the inequality  . Write the solution in set-builder notation.

Accepted Answer

To solve the inequality, we need to isolate the variable on one side of the inequality sign. We can start by subtracting 3eb35c45_86aa_4b78_89e1_d737c02aea66_TB8311_11 from both sides:
11eb69da_9f03_df4c_af94_9d9eb257d322_TB8311_11 - 3eb35c45_86aa_4b78_89e1_d737c02aea66_TB8311_11 < 6 + e7fbf809_c28e_45c3_9015_3f96ee5f98d8_TB8311_11
Simplifying:
11eb69da_9f03_df4c_af94_5fc00166093e_TB8311_11 < 6 + e7fbf809_c28e_45c3_9015_3f96ee5f98d8_TB8311_11
Next, we can simplify the right side of the inequality by adding 6 + e7fbf809_c28e_45c3_9015_3f96ee5f98d8_TB8311_11:
11eb69da_9f03_df4c_af94_5fc00166093e_TB8311_11 < e7fbf809_c28e_45c3_9015_3f96ee5f98d8_ TB8311_11 + 6
11eb69da_9f03_df4c_af94_5fc00166093e_TB8311_11 < e7fbf809_c28e_45c3_9015_3f96ee5f98de_TB8311_11 
Finally, we can convert the inequality to set-builder notation: 
{ x | x < e7fbf809_c28e_45c3_9015_3f96ee5f98de_TB8311_11 }

Question 16

A passenger train leaves a train depot two hours after a freight train leaves the same depot. The freight train is traveling 16 mph slower than the passenger train. Find the rate of the freight train if the passenger train overtakes the freight train after 3.75 h.

Accepted Answer

Let the rate of the freight train be x mph.
Then, the rate of the passenger train is (x+16) mph.
Let the distance traveled by both the trains be the same when the passenger train overtakes the freight train, which is d.
Distance traveled by the freight train in 3.75 hours = d
Distance traveled by the passenger train in 3.75 hours + 2 hours (time difference) = d
=> (x+16)*5.75 = x*3.75
=> 5.75x + 92 = 3.75x
=> 2x = 92
=> x = 46
Therefore, the rate of the freight train = x = 46 mph.

Question 17

Solve the inequality  . Write the solution in set-builder notation.

Accepted Answer

The answer of Solve the inequality  . Write the...

Question 18

Solve the inequality  . Write the solution in interval notation.

Accepted Answer

The answer of Solve the inequality  . Write the...

Question 19

Graph the solution set for the inequality  .

Accepted Answer

The answer of Graph the solution set for the inequality...

Question 20

Solve the inequality  . Write the solution in set-builder notation.

Accepted Answer

Subtracting 5 from both sides, we get 2e - 5 > -6. Adding 5 to both sides, we get 2e > -1. Dividing both sides by 2, we get e > -1/2. The solution is {e | e > -1/2}. This is equivalent to choice C.

Quiz 2: First-Degree Equations and Inequalities

Solve the inequality . Write the solution in set-builder notation.

Solve the inequality . Write the solution in set-builder notation.

Solve the inequality . Write the solution in interval notation.

Graph the solution set for the inequality .

Graph the solution set for the inequality .

Solve the inequality . Write the solution in interval notation.

Graph the solution set for the inequality .

Graph the solution set for the inequality .

At 10 A.M. a plane leaves Boston, Massachusetts, for Seattle, Washington, a distance of 3000 mi. One hour later a plane leaves Seattle for Boston. Both planes are traveling at a speed of 400 mph. How many hours after the plane leaves Seattle will the planes pass each other?

Solve the inequality . Write the solution in set-builder notation.

Graph the solution set for the inequality .

A 565-mile, 5 hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. For the remainder of the trip, the average speed was 125 mph. How long did the plane fly at 105 mph?

Solve the inequality . Write the solution in interval notation.

Solve the inequality . Write the solution in set-builder notation.

Solve the inequality . Write the solution in set-builder notation.

A passenger train leaves a train depot two hours after a freight train leaves the same depot. The freight train is traveling 16 mph slower than the passenger train. Find the rate of the freight train if the passenger train overtakes the freight train after 3.75 h.

Solve the inequality . Write the solution in set-builder notation.

Solve the inequality . Write the solution in interval notation.

Graph the solution set for the inequality .

Solve the inequality . Write the solution in set-builder notation.