Question
Solve each compound inequality 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
2x-5 > 3
2x > 8
Dividing 2 both sides
Solving the second inequality for
Plotting the graph
Final Answer:
Hence, the final inequality is x > 4
Dividing 2 both sides
Solving the second inequality for
Plotting the graph
Final Answer:
Hence, the final inequality is x > 4
On the number line, we can graph the compound inequalities. When graphing compound inequalities, keep the following points in mind.
• Consider a number on the number line that corresponds to the inequality. For example, if x > 2, we must determine where '2' falls on the number line.
• If the inequality is either ">" or "<, "place an open dot (to indicate that the value is "NOT" included).
If the inequality is either "≥" or " ≤, "place a closed dot to include the value.
For example, if x > 2, place an open dot at '2' because the inequality is strict and does not include " =."
• Place an arrow symbol on the right side of the number for the ">" or "≥" sign.
• Place an arrow symbol on the left side of the number for the " <"or " ≤" sign.
• Finally, use the intersection or union, depending on whether "AND" or "OR" is given, to find the final solution.
Related Questions to study
The sum of two expressions is x3 -x2 + 3x- 2. If one of them is x2 + 5x- 6, what is the
other?
The sum of two expressions is x3 -x2 + 3x- 2. If one of them is x2 + 5x- 6, what is the
other?
Find the missing coordinate k if the taxicab distance between (-7, 10) and (k, 5) is 8.
Find the missing coordinate k if the taxicab distance between (-7, 10) and (k, 5) is 8.
Write the compound inequality for the graph :
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Find the taxicab distance between (-5, 7) and (0, 4).
Find the taxicab distance between (-5, 7) and (0, 4).
The length of a rod is 4x + 5y- 3z cm and the length of another is 6x- 3y + z cm. By
How much is the second rod longer than the first?
The length of a rod is 4x + 5y- 3z cm and the length of another is 6x- 3y + z cm. By
How much is the second rod longer than the first?
Kona Graphed the compound inequality x > 2 or x > 3 by graphing x > 3. Explain Kona’s error.
We will use the following steps to solve a system of linear inequalities graphically as per Kona's error described in the question:
1. Determine the inequality for y.
2. Graph the line as a solid or dashed line depending on the sign of the inequality.
• Draw the line as a dashed line if the inequality sign lacks an equals sign (or >).
• If the inequality sign includes an equals sign, draw the line as a solid line (or).
3. Highlight the area that satisfies the inequality.
4. Repeat steps 1–3 for each inequality.
5. The overlapping region of all the inequalities will be the solution set.
Kona Graphed the compound inequality x > 2 or x > 3 by graphing x > 3. Explain Kona’s error.
We will use the following steps to solve a system of linear inequalities graphically as per Kona's error described in the question:
1. Determine the inequality for y.
2. Graph the line as a solid or dashed line depending on the sign of the inequality.
• Draw the line as a dashed line if the inequality sign lacks an equals sign (or >).
• If the inequality sign includes an equals sign, draw the line as a solid line (or).
3. Highlight the area that satisfies the inequality.
4. Repeat steps 1–3 for each inequality.
5. The overlapping region of all the inequalities will be the solution set.
What is the shortest path from the park to the coffee shop?
What is the shortest path from the park to the coffee shop?
Find the product of (x2 + 3x + 5) and (x2 -1).
Find the product of (x2 + 3x + 5) and (x2 -1).
When a < b, how is the graph of x > a and x < b similar to the graph of x > a? How is it different?
At least two inequalities separated by "and" or "or" make up a compound inequality.
¶Most of the time, the solutions can be determined between two quantities. Where sometimes, it goes on for a while in one direction. An example of borderline high blood pressure is the systolic blood pressure range of 120 to 139 mm mercury (Hg).
¶The graph intersection of the inequalities is represented by the graph of a compound inequality with "and." If a particular number resolves both inequalities, it is a solution to the compound inequality. It can be expressed as either x > -1 and x
When a < b, how is the graph of x > a and x < b similar to the graph of x > a? How is it different?
At least two inequalities separated by "and" or "or" make up a compound inequality.
¶Most of the time, the solutions can be determined between two quantities. Where sometimes, it goes on for a while in one direction. An example of borderline high blood pressure is the systolic blood pressure range of 120 to 139 mm mercury (Hg).
¶The graph intersection of the inequalities is represented by the graph of a compound inequality with "and." If a particular number resolves both inequalities, it is a solution to the compound inequality. It can be expressed as either x > -1 and x
Rebecca earns $30 for each item she sells and a 5% commission on each sale she makes. Write an equation to express her earnings in 5 days if she sold 10 items.
Rebecca earns $30 for each item she sells and a 5% commission on each sale she makes. Write an equation to express her earnings in 5 days if she sold 10 items.
The number of gallons of oil in stock decreases at a rate of 800 gallons per day. Initially, there were 9000 gallons of oil in stock. Write the equation to model this situation. After how many days will the store run out of oil?
The number of gallons of oil in stock decreases at a rate of 800 gallons per day. Initially, there were 9000 gallons of oil in stock. Write the equation to model this situation. After how many days will the store run out of oil?
What are compound inequalities and how are their solutions represented?
What are compound inequalities and how are their solutions represented?
Are the lines 6x - 3y = 5 and 2y = - 4x + 4 perpendicular?
Are the lines 6x - 3y = 5 and 2y = - 4x + 4 perpendicular?
Enquire plans a diet for his dog, river. River Consumes between 510 and 540 calories per day. If river eats 1.5 servings of dog food each day, how many treats can she have?
Enquire plans a diet for his dog, river. River Consumes between 510 and 540 calories per day. If river eats 1.5 servings of dog food each day, how many treats can she have?
Solve each compound inequality and graph the solution.
2x+5 > -3 and 4x+7 < 15
Two or more inequalities separated by "and" or "or" make up a compound inequality.
The graph intersection of the inequalities is represented by the graph of a compound inequality with an " and."
A number is a solution to compound inequality if it resolves both inequalities. It can also be written as x > -1 and x < 2 or as -1 < x < 2.
The graph of a compound inequality is the union of the graphs of each inequality. If a number solves at least one of the inequalities, it is a solution to the compound inequality. It is written as x < -1 or x > 2.
Solve each compound inequality and graph the solution.
2x+5 > -3 and 4x+7 < 15
Two or more inequalities separated by "and" or "or" make up a compound inequality.
The graph intersection of the inequalities is represented by the graph of a compound inequality with an " and."
A number is a solution to compound inequality if it resolves both inequalities. It can also be written as x > -1 and x < 2 or as -1 < x < 2.
The graph of a compound inequality is the union of the graphs of each inequality. If a number solves at least one of the inequalities, it is a solution to the compound inequality. It is written as x < -1 or x > 2.
