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We have successfully offered the best assignment help on MyMathlab Answers 2020, and now we look forward to the upcoming years. We have the most experienced group for mymathlab answers, and their capabilities are ridiculously excellent. It can be an essay, a test, or a quiz; these individuals are specialists and can tackle any MyMathLab assignment help. Here’s a sample list of questions and answers:
Q.1) Solve the compound inequality.
5x−6<−1 and −4x+5>21
Ans:
To solve a compound inequality involving “and,” we solve each inequality separately and then find the intersection of the solution sets
Isolate the variable term using the addition property of inequalities.
5x – 6 < -1
Or, 5x -6 +6 < -1 +6 [adding 6 to both sides]
Or, 5x < 5
Or, x < 1 [ dividing by 5 on both sides]
Now solve the second inequality. Isolate the variable term using the addition property of inequalities.
-4x+5 > 21
Or, -4x +5 -5 > 21 -5 [ adding -5 to both sides]
Or, -4x > 16
Or, x < -4 [ dividing by -4 on both sides and signs reversed ]
Now we know, The intersection of two sets A and B is the set of all elements that belong to both set A and set B. The solution interval must satisfy both x<1 and x <-4 .
Hence the solution in interval notation be ( – ∞, -4)
Q.2) Express the set in the simplest interval form.
(−∞,−1] ∩ [−2,∞)
Ans:
This interval represents the intersection of two intervals.
Instead of the symbol ∩, the connector “and” might be used.
Thus the intersection consists of points that are in both (−∞,−1]and [−6, ∞).
There is no gap between these two intervals.
The interval that represents the intersection of the given intervals has two endpoints, −1 and −2
The single interval that consists (−∞,−1] ∩ [−2,∞) is [ -2, -1]
Q.3) The monthly expenses for two offices are shown in the table to the right. Which of the three expenses are in the set of expenses that are greater than $2600 for the Chicago office and less than $2800 for the Tokyo office?
Ans:
Type of Expense
Rent
Chicago-$2309
Tokyo-$8081
Insurance-
Chicago-$210
Tokyo-$266
Housekeeping-
Chicago-$388
Tokyo-$311
Expenses that belong in the set are greater than
$2600 for the Chicago office and less than $2800 for the Tokyo office.
None of the three expenses is greater than $2600 for the Chicago office.
Housekeeping and insurance are less than $2800 for the Tokyo office.
Hence, There are no expenses that are both greater than $2600 for the Chicago office and less than $2800 for the Tokyo office.
So, The set of expenses that are greater than $3000 for the Chicago office and less than $2900 for the Tokyo office is ∅ (empty set)
Q.4) Solve the following inequality |−4x+10| ≤ 5
Ans: Write the absolute value inequality as an equivalent compound inequality. The absolute value of a number is the number’s distance from 0 on the number line.
According to this definition,
|−4x+10|≤5 means that the expression −4x+10 represents a number that is less than or equal to 5 units from 0 on either side of the number line.
As a result, the following is the equivalent compound inequality.
−5≤−4x+10≤5
Now solve this inequality for x.
In order to isolate the x-term in the middle, subtract 10 from each part.
−5−10≤−4x≤5−10
Or, −15≤−4x≤−5
To isolate x in the middle, divide each part by
−4.
When dividing by a negative number, be sure to reverse the direction of each inequality symbol.
-15/-4 >_X _< -5/-4
It may be helpful to rewrite the inequality in the following form so that the smallest number is on the left and the largest is on the right.
15/4 >_X _< 5/4
The solution in interval notation is [5/4,15/4]
We have successfully offered the best assignment help on MyMathlab Answers 2020, and now we look forward to the upcoming years. We have the most experienced group for mymathlab answers, and their capabilities are ridiculously excellent. It can be an essay, a test, or a quiz; these individuals are specialists and can tackle any MyMathLab assignment help. Here’s a sample list of questions and answers:
Q.1) Solve the compound inequality.
5x−6<−1 and −4x+5>21
Ans:
To solve a compound inequality involving “and,” we solve each inequality separately and then find the intersection of the solution sets
Isolate the variable term using the addition property of inequalities.
5x – 6 < -1
Or, 5x -6 +6 < -1 +6 [adding 6 to both sides]
Or, 5x < 5
Or, x < 1 [ dividing by 5 on both sides]
Now solve the second inequality. Isolate the variable term using the addition property of inequalities.
-4x+5 > 21
Or, -4x +5 -5 > 21 -5 [ adding -5 to both sides]
Or, -4x > 16
Or, x < -4 [ dividing by -4 on both sides and signs reversed ]
Now we know, The intersection of two sets A and B is the set of all elements that belong to both set A and set B. The solution interval must satisfy both x<1 and x <-4 .
Hence the solution in interval notation be ( – ∞, -4)
Q.2) Express the set in the simplest interval form.
(−∞,−1] ∩ [−2,∞)
Ans:
This interval represents the intersection of two intervals.
Instead of the symbol ∩, the connector “and” might be used.
Thus the intersection consists of points that are in both (−∞,−1]and [−6, ∞).
There is no gap between these two intervals.
The interval that represents the intersection of the given intervals has two endpoints, −1 and −2
The single interval that consists (−∞,−1] ∩ [−2,∞) is [ -2, -1]
Q.3) The monthly expenses for two offices are shown in the table to the right. Which of the three expenses are in the set of expenses that are greater than $2600 for the Chicago office and less than $2800 for the Tokyo office?
| Type of Expense | Chicago | Tokyo | ||
| Rent | $2309 | $8081 | ||
| Insurance | $210 | $266 | ||
| Housekeeping | $388 | $311 | ||
Ans:
Expenses that belong in the set are greater than
$2600 for the Chicago office and less than $2800 for the Tokyo office.
None of the three expenses is greater than $2600 for the Chicago office.
Housekeeping and insurance are less than $2800 for the Tokyo office.
Hence, There are no expenses that are both greater than $2600 for the Chicago office and less than $2800 for the Tokyo office.
So, The set of expenses that are greater than $3000 for the Chicago office and less than $2900 for the Tokyo office is ∅ (empty set)
Q.4) Solve the following inequality |−4x+10| ≤ 5
Ans: Write the absolute value inequality as an equivalent compound inequality. The absolute value of a number is the number’s distance from 0 on the number line.
According to this definition,
|−4x+10|≤5 means that the expression −4x+10 represents a number that is less than or equal to 5 units from 0 on either side of the number line.
As a result, the following is the equivalent compound inequality.
−5≤−4x+10≤5
Now solve this inequality for x.
In order to isolate the x-term in the middle, subtract 10 from each part.
−5−10≤−4x≤5−10
Or, −15≤−4x≤−5
To isolate x in the middle, divide each part by
−4.
When dividing by a negative number, be sure to reverse the direction of each inequality symbol.
-15/-4 >_X _< -5/-4
It may be helpful to rewrite the inequality in the following form so that the smallest number is on the left and the largest is on the right.
15/4 >_X _< 5/4
The solution in interval notation is [5/4,15/4]
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