Question
Fatima plans to spend at least $15 and at most $ 20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range?
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, Fatima can buy 12 to 18 pencils while staying in her price range.
Fatima bought 2 sketch pads.
Cost of two sketch pads = 2 $3.25 = $6.5
Fatima can spend at least $15 and at most $ 20. Let’s say the number of pens Fatima bought is n.
So, Total money spent by Fatima = $(6.5 + 0.75n)
Now, $15 ≤ $(6.5 + 0.75n) ≤ $20
Solving the inequality
15 ≤ 6.5 + 0.75n ≤ 20
Subtracting 6.5 on all sides
8.5 ≤ 0.75n ≤ 13.5
Dividing 0.75 on all sides
11.33 ≤ n ≤ 18 or 12 ≤ n ≤ 18
Final Answer:
Hence, Fatima can buy 12 to 18 pencils while staying in her price range.
Subtracting 6.5 on all sides
Dividing 0.75 on all sides
Final Answer:
Hence, Fatima can buy 12 to 18 pencils while staying in her price range.
Inequalities define the relationship between two non-equal values. Inequality means not being equal. In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to a sign (≥), less than or equal to a symbol (≤), and not equivalent to a symbol (≠). Many can solve simple inequalities in math by multiplying, dividing, adding, or subtracting both sides until left with the variable.
The compound inequality in this question is solved with the following instructions:
• Let us suppose Fatima purchased 'n' pens.
• Calculating the total money spent on the pens.
• Then solve the inequality by subtraction and division on all sides.
• As a result, you get the answer to how much Fatima spends on pencils while staying within her price range.
Related Questions to study
Find the antonym of the underlined word After the car accident ,his memories were quite nebulous.
Find the antonym of the underlined word After the car accident ,his memories were quite nebulous.
What is the meaning of the prefix-sub
What is the meaning of the prefix-sub
Write a compound inequality to represent the sentence below:
A Quantity x is either less than 10 or greater than 20.
An inequality with a linear function included is referred to as a linear inequality. When the word "and" connects two inequalities, the solution takes place when both inequalities hold true at the same moment. The solution, however, only applies when one of the two inequalities is true when the two are connected by the word "or." The combination or union of the two separate solutions is the solution. When two simple inequalities are combined using either "AND" or "OR," the result is a compound inequality.
One of the two claims is proven to be true by the compound inequality with "AND." If the answers to the separate statements of the compound inequality overlap. While "Or" means that the entire compound sentence is true as long as either of the two statements is true. The solution sets for the various statements are united to form this concept.
Write a compound inequality to represent the sentence below:
A Quantity x is either less than 10 or greater than 20.
An inequality with a linear function included is referred to as a linear inequality. When the word "and" connects two inequalities, the solution takes place when both inequalities hold true at the same moment. The solution, however, only applies when one of the two inequalities is true when the two are connected by the word "or." The combination or union of the two separate solutions is the solution. When two simple inequalities are combined using either "AND" or "OR," the result is a compound inequality.
One of the two claims is proven to be true by the compound inequality with "AND." If the answers to the separate statements of the compound inequality overlap. While "Or" means that the entire compound sentence is true as long as either of the two statements is true. The solution sets for the various statements are united to form this concept.
Which word has long a sound ?
Which word has long a sound ?
Write a compound inequality to represent the sentence below: A Quantity x is at least 10 and at most 20.
Write a compound inequality to represent the sentence below: A Quantity x is at least 10 and at most 20.
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.
