Question
What are compound inequalities and how are their solutions represented?
The correct answer is: x < 4 and x > –3
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.
For example
3 x + 2 < 14 and 2 x – 5 > –11
3 x < 12 and 2 x > –6
x < 4 and x > –3
Related Questions to study
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.
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?
Evaluate the expression 81p2 + 16q2 - 72pq when P = 
and q =
Evaluate the expression 81p2 + 16q2 - 72pq when P = and q =
Write a compound inequality for each graph:
Write a compound inequality for each graph:
Solve the compound inequality: -12 ≤ 7x + 9 < 16 and graph the solution
Solve the compound inequality: -12 ≤ 7x + 9 < 16 and graph the solution
Observe the diagram carefully and find x and y.
Observe the diagram carefully and find x and y.
Observe the given window and explain which lines are parallel.
Observe the given window and explain which lines are parallel.
Find the value of x.
Find the value of x.
Ajit is 21 years younger than his father. What is their total age in 7 years' time?
Ajit is 21 years younger than his father. What is their total age in 7 years' time?
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}
Solve the compound inequality -3x + 2 > -7 or 2(x - 2) ≥ 6. Graph the solution:
The combination of two inequalities using "and" or "or" results in a compound inequality. Each inequality in a compound inequality can be solved using the same steps as a normal inequality, but when combining the solutions, it makes a difference whether "and" or "or" is used to join the two inequality solutions together.
¶For instance, 1 < x < 3 is equivalent to "x > 1 andx < 3". The use of "or" is always used to specifically refer to a compound inequality, on the other hand.
¶x > 1: Since there is no "=" at 1, we receive an open dot. Additionally, since 1 has ">," we draw an arrow to the right of it.
Solve the compound inequality -3x + 2 > -7 or 2(x - 2) ≥ 6. Graph the solution:
The combination of two inequalities using "and" or "or" results in a compound inequality. Each inequality in a compound inequality can be solved using the same steps as a normal inequality, but when combining the solutions, it makes a difference whether "and" or "or" is used to join the two inequality solutions together.
¶For instance, 1 < x < 3 is equivalent to "x > 1 andx < 3". The use of "or" is always used to specifically refer to a compound inequality, on the other hand.
¶x > 1: Since there is no "=" at 1, we receive an open dot. Additionally, since 1 has ">," we draw an arrow to the right of it.
