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 result is that x belongs to all real number.
Solving the first inequality for x
-x+1 > -2
-x > -3
Dividing -1 both sides
x < 3
Solving the second inequality for x
6(2x-3) ≥ -6
Dividing 6 both sides
2x-3 ≥ -1
2x ≥ 2
Dividing 2 both sides
x ≥ 1
So, the final result is x < 3 or x ≥ 1
Plotting the graph
Final Answer:
Hence, the final result is that belongs to all real number.
Dividing -1 both sides
Solving the second inequality for x
Dividing 6 both sides
Dividing 2 both sides
So, the final result is x < 3 or x ≥ 1
Plotting the graph
Final Answer:
Hence, the final result is that belongs to all real number.
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Solve each compound inequality and graph the solution
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.
Solve each compound inequality and graph the solution
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.
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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.
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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.
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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
