Question
When a < b, how is the graph of x > a and x < b similar to the graph of x > a? How is it different?
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 difference between the graphs of x > a and x < b & x > a is that in x > a numbers after b are also the solution but in x > a and x < b, the solutions is between a and b.
If a < b, then in number line a will be anywhere on the left-hand side of b.
So, plotting the graph for inequality x > a and x < b
As the statements are joined by “And”. So, the final graph will be
The graph for x > a is
Final Answer:
Hence, the difference between the graphs of x > a and x < b & x > a is that in x > a numbers after b are also the solution but in x > a and x < b, the solutions is between a and b.
As the statements are joined by “And”. So, the final graph will be
The graph for x > a is
Final Answer:
Hence, the difference between the graphs of x > a and x < b & x > a is that in x > a numbers after b are also the solution but in x > a and x < b, the solutions is between a and b.
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
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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.
What is the perpendicular distance between two parallel lines 4x + 3y = 6 and 8x+ 6y = - 3?
What is the perpendicular distance between two parallel lines 4x + 3y = 6 and 8x+ 6y = - 3?
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and q =
Evaluate the expression 81p2 + 16q2 - 72pq when P = and q =
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Solve each compound inequality and graph the solution.
2x+5 > -3 and 4x+7 < 15
When two inequality statements are joined by the words "or" or "and," the sentence is said to be compound inequality. The preposition "and" denotes that both statements in the compound sentence are true simultaneously. It is where the solution sets for the several statements to cross or overlap. The conjunction "or" indicates that the whole compound statement is true.
Example
Solve for x: 3 x + 2 < 14 and 2 x – 5 > –11
Here we have to solve each inequality individually. Because the joining word is "and," the overlap or intersection is the desired outcome.
3x+2<14 and 2x-5>-11
3x<12 2x>-6
x<4 x>-3
Numbers to the left of 4 are represented by x < 4, and the right of -3 is represented by x > -3. The solution set consists of {x| x > –3 and x < 4}
Solve each compound inequality and graph the solution.
2x+5 > -3 and 4x+7 < 15
When two inequality statements are joined by the words "or" or "and," the sentence is said to be compound inequality. The preposition "and" denotes that both statements in the compound sentence are true simultaneously. It is where the solution sets for the several statements to cross or overlap. The conjunction "or" indicates that the whole compound statement is true.
Example
Solve for x: 3 x + 2 < 14 and 2 x – 5 > –11
Here we have to solve each inequality individually. Because the joining word is "and," the overlap or intersection is the desired outcome.
3x+2<14 and 2x-5>-11
3x<12 2x>-6
x<4 x>-3
Numbers to the left of 4 are represented by x < 4, and the right of -3 is represented by x > -3. The solution set consists of {x| x > –3 and x < 4}
