Question
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
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: The graph of x > a and x > b does not include the region from a to b while it is included in the graph of x > a or x > b.
If a < b, then in number line a will be anywhere on the left-hand side of b.
The graph for the inequality x > a and x > b is given as
The graph for the inequality x > a or x > b is given as
Final Answer:
The graph of x > a and x > b does not include the region from a to b while it is included in the graph of x > a or x > b.
The graph for the inequality x > a or x > b is given as
Final Answer:
The graph of x > a and x > b does not include the region from a to b while it is included in the graph of x > a or x > b.
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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.
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To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
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Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. write and solve a compound inequality to model the possible length of the dog run.
Follow the same steps as when solving equations to solve compound inequalities. However, because compound inequalities are composed of two inequalities, separate them and solve each inequity separately. Once the inequalities are separated, isolate the variable using the inverse operation, similar to how equations are solved.
For example, to solve the compound inequality 14 > 2x > 4, do the following:
14 > 2x > 4
The two inequalities are separated by 14 > 2x and 2x > 4.
To isolate the variable, divide both sides by 2: 14/2 > 2x/2 and 2x/2 > 4/2.
7 > x and x > 2 are now two sets of solutions.
7 > x > 2, the possible answers range from 2 to 7.
Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. write and solve a compound inequality to model the possible length of the dog run.
Follow the same steps as when solving equations to solve compound inequalities. However, because compound inequalities are composed of two inequalities, separate them and solve each inequity separately. Once the inequalities are separated, isolate the variable using the inverse operation, similar to how equations are solved.
For example, to solve the compound inequality 14 > 2x > 4, do the following:
14 > 2x > 4
The two inequalities are separated by 14 > 2x and 2x > 4.
To isolate the variable, divide both sides by 2: 14/2 > 2x/2 and 2x/2 > 4/2.
7 > x and x > 2 are now two sets of solutions.
7 > x > 2, the possible answers range from 2 to 7.
