Question
Write a compound inequality to represent the sentence below: A Quantity x is at least 10 and at most 20.
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 compound inequality is 10 ≤ x ≤ 20.
It is given that x is at least 10 or we can say x is greater than or equal to 10 and in mathematical terms it can be written as
x ≥ 10
Also, It is given that x is at most 20 or we can say x is less than or equal to 20 and in mathematical terms it can be written as
x ≤ 20
The graph can be plotted for both inequalities as
As “And” is used between the statements. So, the compound inequality can be written as 10 ≤ x ≤ 20
Final Answer:
Hence, the compound inequality is 10 ≤ x ≤ 20.
Also, It is given that x is at most 20 or we can say x is less than or equal to 20 and in mathematical terms it can be written as
The graph can be plotted for both inequalities as
As “And” is used between the statements. So, the compound inequality can be written as 10 ≤ x ≤ 20
Final Answer:
Hence, the compound inequality is 10 ≤ x ≤ 20.
Related Questions to study
The value for area A of each figure is given. Write and solve a compound inequality for the value of x in each figure.
9 ≤ A ≤ 12
Here is a list of some key points to remember when studying triangle inequality:
• The Triangle Inequality theorem states that the sum of any two sides of a triangle must be greater than the sum of the third side.
• In a triangle, two arcs will intersect if the sum of their radii is greater than the distance between their centres.
• If the sum of any two sides of a triangle is greater than the third, the difference of any two sides will be less than the third.
The value for area A of each figure is given. Write and solve a compound inequality for the value of x in each figure.
9 ≤ A ≤ 12
Here is a list of some key points to remember when studying triangle inequality:
• The Triangle Inequality theorem states that the sum of any two sides of a triangle must be greater than the sum of the third side.
• In a triangle, two arcs will intersect if the sum of their radii is greater than the distance between their centres.
• If the sum of any two sides of a triangle is greater than the third, the difference of any two sides will be less than the third.
The value for area A of each figure is given. Write and solve a compound inequality for the value of x in each figure. 35 ≥ A ≥ 25
The value for area A of each figure is given. Write and solve a compound inequality for the value of x in each figure. 35 ≥ A ≥ 25
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
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
Solve each compound inequality and graph the solution
Solve each compound inequality and graph the solution
Suppose that a < b. Select from the symbols <, >, ≥, ≤ as well as the words and & or to complete the compound inequality below so that its solution is all real numbers
x a X b
The compound inequality solution is x > 3 or x ≤ 4 and is the set of all real numbers. As shown in the example below, one needs to solve one or more inequalities before determining the solution to the compound inequality. Solve each inequality by removing the variable.
An inequality with all real numbers as solutions is simple to solve or identify. Here is an example.
Example
Solve x - x > -1
x - x > -1
Because x - x = 0, we get 0 > -1.
This inequality holds because 0 is always greater than -1. As a result, all real numbers are solutions.
Suppose that a < b. Select from the symbols <, >, ≥, ≤ as well as the words and & or to complete the compound inequality below so that its solution is all real numbers
x a X b
The compound inequality solution is x > 3 or x ≤ 4 and is the set of all real numbers. As shown in the example below, one needs to solve one or more inequalities before determining the solution to the compound inequality. Solve each inequality by removing the variable.
An inequality with all real numbers as solutions is simple to solve or identify. Here is an example.
Example
Solve x - x > -1
x - x > -1
Because x - x = 0, we get 0 > -1.
This inequality holds because 0 is always greater than -1. As a result, all real numbers are solutions.
Solve each compound inequality and graph the solution
Solve each compound inequality and graph the solution
Describe and correct the error a student made graphing the compound inequality x ≥ 2 and x > 4
A graph of a compound inequality with a "or" shows how the graphs of the individual inequalities are combined. If a number solves any of the inequalities, then it is a solution to the compound inequality. A compound inequality results from the combination of two simple inequality problems. Steps on Graphing compound Inequalities
1. Reconcile every inequality. 6x−3<9. ...
2. Graph every response. The numbers that prove both inequalities are plotted. The final graph will display all the values—the values shaded on both of the first two graphs— true for both inequalities.
3. Use interval notation to write out the answer. [−3,2)
¶
Describe and correct the error a student made graphing the compound inequality x ≥ 2 and x > 4
A graph of a compound inequality with a "or" shows how the graphs of the individual inequalities are combined. If a number solves any of the inequalities, then it is a solution to the compound inequality. A compound inequality results from the combination of two simple inequality problems. Steps on Graphing compound Inequalities
1. Reconcile every inequality. 6x−3<9. ...
2. Graph every response. The numbers that prove both inequalities are plotted. The final graph will display all the values—the values shaded on both of the first two graphs— true for both inequalities.
3. Use interval notation to write out the answer. [−3,2)
¶
Line 1: passes through (0, 1) and (-1, 5)
Line 2: passes through (7, 2) and (3, 1)
Line1 and line 2 are
Line 1: passes through (0, 1) and (-1, 5)
Line 2: passes through (7, 2) and (3, 1)
Line1 and line 2 are
The compound inequality x > a and x > b is graphed below. How is the point labelled c related to a and b?
When working with inequalities, we can treat them similarly to, but not identically to, equations. We can use the addition and multiplication properties to help us solve them. The inequality symbol must be reversed when dividing or multiplying by a negative number. This question concluded that inequalities have the following properties:
A GENERAL NOTE: PROPERTIES OF INEQUALITIES
Addition Property: If a<b, then a + c < b + c.
Multiplication Property: If a < b and c > 0, then ac < b c and a<b and c < 0, then ac > bc.
These properties also apply to a ≤ b, a > b, and a ≥ b.
The compound inequality x > a and x > b is graphed below. How is the point labelled c related to a and b?
When working with inequalities, we can treat them similarly to, but not identically to, equations. We can use the addition and multiplication properties to help us solve them. The inequality symbol must be reversed when dividing or multiplying by a negative number. This question concluded that inequalities have the following properties:
A GENERAL NOTE: PROPERTIES OF INEQUALITIES
Addition Property: If a<b, then a + c < b + c.
Multiplication Property: If a < b and c > 0, then ac < b c and a<b and c < 0, then ac > bc.
These properties also apply to a ≤ b, a > b, and a ≥ b.
Solve each compound inequality and graph the solution
2x-5 > 3 and -4x+7 < -25
Divide a compound inequality into two individual inequalities before solving it. The solution should either be a union of sets ("or") or an intersection of sets ("and"). After that, resolve the graph and all inequalities.
Use the steps below to resolve an inequality:
Step 1: Fractions are first eliminated by multiplying all terms by the total fractions' lowest common denominator.
Step 2: Simplify the inequality by combining like terms on each side.
Step 3: Subtract or add quantities to get the unknown on one side and the numbers on the other.
Solve each compound inequality and graph the solution
2x-5 > 3 and -4x+7 < -25
Divide a compound inequality into two individual inequalities before solving it. The solution should either be a union of sets ("or") or an intersection of sets ("and"). After that, resolve the graph and all inequalities.
Use the steps below to resolve an inequality:
Step 1: Fractions are first eliminated by multiplying all terms by the total fractions' lowest common denominator.
Step 2: Simplify the inequality by combining like terms on each side.
Step 3: Subtract or add quantities to get the unknown on one side and the numbers on the other.
The slope of line a is – 4. Line b is perpendicular to line a. The equation of line c is 3y + 12x = 6. What is the relation between line b and line c?
The slope of line a is – 4. Line b is perpendicular to line a. The equation of line c is 3y + 12x = 6. What is the relation between line b and line c?
Nadeem plans to ride her bike between 12 mi and 15 mi. Write and solve an inequality to model how many hours Nadeem will be riding?
In this question, the time taken to ride by Nadeem is to be calculated with the help of the speed and distance formula (time = distance/speed). So, for example, to determine the time required to complete a journey, we must first know the distance and speed.
There are three different ways to write the formula. They are:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
Calculating with the time formula gives us the answer as an inequality.
Nadeem plans to ride her bike between 12 mi and 15 mi. Write and solve an inequality to model how many hours Nadeem will be riding?
In this question, the time taken to ride by Nadeem is to be calculated with the help of the speed and distance formula (time = distance/speed). So, for example, to determine the time required to complete a journey, we must first know the distance and speed.
There are three different ways to write the formula. They are:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
Calculating with the time formula gives us the answer as an inequality.
Solve each compound inequality and graph the solution:
2(4x + 3) ≥ -10 or -5x - 15 > 5
Solve each compound inequality and graph the solution:
2(4x + 3) ≥ -10 or -5x - 15 > 5
Solve each compound inequality and graph the solution
-x+1 > -2 and 6(2x-3) ≥ -6
Solve each compound inequality and graph the solution
-x+1 > -2 and 6(2x-3) ≥ -6
Solve each compound inequality and graph the solution:
4x - 1 > 3 and -2(3x - 4) ≥ -16
Inequalities define the relationship between two values that are not equal. Not equal is the definition of inequality. In most cases, we use the "not equal symbol (≠)" to indicate that two values are not equal. But several inequalities are employed to compare the values, whether they are less than or more.
Step 1: The values on the number line that satisfy each inequality in the compound inequality are shaded on the graph. The graph's endpoint should be marked with a filled-in circle to show that a value included in the inequality symbol is either or; otherwise, the endpoint should be marked with an open circle to show that a value is not included. There should be an arrow pointing in that direction at the end of the graph that never ends.
Step 2: The graph of the compound inequality is the intersection of the two graphs from Step 1 if the compound inequality contains the term AND. Only the portion of the number line that appears in both graphs should be shaded. The graph of the compound inequality is the union of the two graphs from Step 1 if the compound inequality contains the term OR. Incorporate both of these graphs into the last one.
Solve each compound inequality and graph the solution:
4x - 1 > 3 and -2(3x - 4) ≥ -16
Inequalities define the relationship between two values that are not equal. Not equal is the definition of inequality. In most cases, we use the "not equal symbol (≠)" to indicate that two values are not equal. But several inequalities are employed to compare the values, whether they are less than or more.
Step 1: The values on the number line that satisfy each inequality in the compound inequality are shaded on the graph. The graph's endpoint should be marked with a filled-in circle to show that a value included in the inequality symbol is either or; otherwise, the endpoint should be marked with an open circle to show that a value is not included. There should be an arrow pointing in that direction at the end of the graph that never ends.
Step 2: The graph of the compound inequality is the intersection of the two graphs from Step 1 if the compound inequality contains the term AND. Only the portion of the number line that appears in both graphs should be shaded. The graph of the compound inequality is the union of the two graphs from Step 1 if the compound inequality contains the term OR. Incorporate both of these graphs into the last one.
