Question
Solve -24 < 4x-4 < 4. 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 -5 < x < 2
-24 < 4x-4 < 4
adding 4 on all sides
-24 + 4 < 4x < 4 + 4
-20 < 4x < 8
Dividing 5 on all sides
-5 < x < 2
Plotting the graph
Final Answer:
Hence, the final inequality is -5 < x < 2
adding 4 on all sides
Dividing 5 on all sides
Plotting the graph
Final Answer:
Hence, the final inequality is -5 < x < 2
Related Questions to study
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.
