Question
Solve x-6 ≤ 18 and 3-2x ≥ 11, and graph the solution.
Hint:
If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality. For example, x>5 (x should be greater than 5).
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. “Or” indicates that, as long as either statement is true, the entire compound sentence is true.
If the symbol is (≥ or ≤) then you fill in the dot and if the symbol is (> or <) then you do not fill in the dot.
The correct answer is: Hence, the final inequality is x ≤ -4.
Solving the first inequality for x
x-6 ≤ 18
x ≤ 24
Solving the second inequality for x
3-2x ≥ 11
- 2x ≥ 8
Dividing -2 both sides
x ≤ -4
So, the final result is x ≤ 24 and x ≤ -4
Plotting the graph
Final Answer:
Hence, the final inequality is x ≤ -4.
Solving the second inequality for x
Dividing -2 both sides
So, the final result is x ≤ 24 and x ≤ -4
Plotting the graph
Final Answer:
Hence, the final inequality is x ≤ -4.
Related Questions to study
Write a compound inequality for each graph:
Write a compound inequality for each graph:
Solve 2x-3 > 5 or 3x-1 < 8 , graph the solution.
A compound inequality is a clause that consists of two inequality statements connected by the words "or" or "and." The conjunction "and" indicates that the compound sentence's two statements are true simultaneously. It is the point at which the solution sets for the various statements overlap or intersect.
¶A type of inequality with two or more parts is a compound inequality. These components may be "or" or "and" statements. If your inequality reads, "x is greater than 5 and less than 10," for instance, x could be any number between 5 and 10.
Solve 2x-3 > 5 or 3x-1 < 8 , graph the solution.
A compound inequality is a clause that consists of two inequality statements connected by the words "or" or "and." The conjunction "and" indicates that the compound sentence's two statements are true simultaneously. It is the point at which the solution sets for the various statements overlap or intersect.
¶A type of inequality with two or more parts is a compound inequality. These components may be "or" or "and" statements. If your inequality reads, "x is greater than 5 and less than 10," for instance, x could be any number between 5 and 10.
If a man goes 15 m due north and then 8 m due east, then his distance from the starting point is ……..
If a man goes 15 m due north and then 8 m due east, then his distance from the starting point is ……..
Write a compound inequality for each graph:
Write a compound inequality for each graph:
Consider the solutions of the compound inequalities.
4 < x < 8 2 < x < 11
Describe each solution as a set. Is one set a subset of the other? Explain your answer.
A compound inequality is a sentence that contains two inequality statements separated by the words "or" or "and." The term "and" indicates that both of the compound sentence's statements are true simultaneously. The intersection of the solutions of two inequalities joined by the word and the solution of a compound inequality. All of the solutions having the two inequalities in common are the solutions to a compound inequality, where the two graphs overlap, as we saw in the previous sections.
¶The graph of a compound inequality with a "and" denotes the intersection of the inequalities' graphs. If a number solves both inequalities, it solves the compound inequality. It can be written as x > -1 and x < 2 or as -1 < x < 2.
¶Graph the compound inequality x > 1 AND x ≤ 4.
Consider the solutions of the compound inequalities.
4 < x < 8 2 < x < 11
Describe each solution as a set. Is one set a subset of the other? Explain your answer.
A compound inequality is a sentence that contains two inequality statements separated by the words "or" or "and." The term "and" indicates that both of the compound sentence's statements are true simultaneously. The intersection of the solutions of two inequalities joined by the word and the solution of a compound inequality. All of the solutions having the two inequalities in common are the solutions to a compound inequality, where the two graphs overlap, as we saw in the previous sections.
¶The graph of a compound inequality with a "and" denotes the intersection of the inequalities' graphs. If a number solves both inequalities, it solves the compound inequality. It can be written as x > -1 and x < 2 or as -1 < x < 2.
¶Graph the compound inequality x > 1 AND x ≤ 4.
Describe and correct the error a student made graphing the compound inequality x>3 or x <-1
Describe and correct the error a student made graphing the compound inequality x>3 or x <-1
Solve -24 < 4x-4 < 4. Graph the solution.
Solve -24 < 4x-4 < 4. Graph the solution.
Let a and b be real numbers. If a = b, how is the graph of x > a and x > b different from the graph of x > a or x > b
When the two expressions are not equal and related to each other, known as inequality. They are denoted by a sign like ≠ “not equal to,” > “greater than,” or < “less than.”.
If a and b have polynomial equations, then there will be a curve between a and b:
- [ b < x < a ]
It will be a line between a and b x > a and x < b if the equations for a and b are linear.
b < x < a
Let a and b be real numbers. If a = b, how is the graph of x > a and x > b different from the graph of x > a or x > b
When the two expressions are not equal and related to each other, known as inequality. They are denoted by a sign like ≠ “not equal to,” > “greater than,” or < “less than.”.
If a and b have polynomial equations, then there will be a curve between a and b:
- [ b < x < a ]
It will be a line between a and b x > a and x < b if the equations for a and b are linear.
b < x < a
Let a and b be real numbers. If a < b, how is the graph of x > a and x > b different from the graph of x > a or x > b
Let a and b be real numbers. If a < b, how is the graph of x > a and x > b different from the graph of x > a or x > b
100 % of students who use their class time wisely complete their project and are successful is an example of __________-
100 % of students who use their class time wisely complete their project and are successful is an example of __________-
Identify the group of words The boy on the porch.
Identify the group of words The boy on the porch.
Which modal verb is best suited for the blank in the sentence? You ______-wash the dishes in cold water.
Which modal verb is best suited for the blank in the sentence? You ______-wash the dishes in cold water.
An animal shelter categorizes donors based on their total yearly donation, as shown in the table.
Keenan donates the same amount each month. Write and solve a compound inequality for the monthly donation that will put him in the gold category.
A compound inequality is a solution that involves or includes the solutions to one inequality and the solutions to the other inequality, x<a or x>b. The compound inequality solution includes only solutions to both inequalities where they coincide. x<a and x>b=>a<x<b. It comprises two inequalities linked together by the words "and" or "or." Compound inequalities are inequalities that have two or more parts. These parts can be either "or" or "and."
For example, if an inequality states that "x is greater than '5' but less than 10," then x could be any number between 5 and 10. To solve a compound inequality, you must find all the variable values that make the compound inequality true. We solve each inequality individually and then compare the two solutions.
An animal shelter categorizes donors based on their total yearly donation, as shown in the table.
Keenan donates the same amount each month. Write and solve a compound inequality for the monthly donation that will put him in the gold category.
A compound inequality is a solution that involves or includes the solutions to one inequality and the solutions to the other inequality, x<a or x>b. The compound inequality solution includes only solutions to both inequalities where they coincide. x<a and x>b=>a<x<b. It comprises two inequalities linked together by the words "and" or "or." Compound inequalities are inequalities that have two or more parts. These parts can be either "or" or "and."
For example, if an inequality states that "x is greater than '5' but less than 10," then x could be any number between 5 and 10. To solve a compound inequality, you must find all the variable values that make the compound inequality true. We solve each inequality individually and then compare the two solutions.
