Question
Lucy plans to spend between $50 and $ 65, inclusive on packages of charms. If she buy 5 packages of beads at $4.95 each, how many packages of charms at $6.55 can lucy buy while staying within her budget?
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, Lucy can buy 4 to 6 charms staying within her budget.
Lucy bought 5 packages of beads
Cost of 5 packages of beads = $4.95 5 = $24.75
Let’s say that number of packages of charms bought by Lucy is n
Cost of n packets of charms = $6.55n
Total money spent by Lucy = $(6.55n + 24.75)
It is given that Lucy can spend between $50 and $ 65
So, $50 ≤ $(6.55n + 24.75) ≤ $65
Solving the inequality
50 ≤ 6.55n + 24.75 ≤ 65
Subtracting 24.75 on all sides
25.25 ≤ 6.55n ≤ 40.25
Dividing 6.55 on all sides
3.85 ≤ n ≤ 6.14 or 4 ≤ n ≤ 6
Final Answer:
Hence, Lucy can buy 4 to 6 charms staying within her budget.
When two simple inequalities are combined, the result is a compound inequality. For example, a sentence with two inequality statements connected by the words "or" or "and" is a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. So it is when the solution sets for the various statements cross over or intersect. E.g., for "AND": Solve the statement where x: 3 x + 2 < 14 and 2 x – 5 > –11. The solution set is
{ x| x > –3 and x < 4}. All the numbers present to the left of 4 are denoted by x < 4, and the numbers to the right of -3 are represented by x > -3. The intersection of these two graphs is comprised of all integers between -3 and 4.
Related Questions to study
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A compound inequality is a clause that consists of two inequality statements connected by the words "or" or "and." The conjunction "and" indicates that the compound sentence's two statements are true simultaneously. It is the point at which the solution sets for the various statements overlap or intersect.
¶A type of inequality with two or more parts is a compound inequality. These components may be "or" or "and" statements. If your inequality reads, "x is greater than 5 and less than 10," for instance, x could be any number between 5 and 10.
Solve 2x-3 > 5 or 3x-1 < 8 , graph the solution.
A compound inequality is a clause that consists of two inequality statements connected by the words "or" or "and." The conjunction "and" indicates that the compound sentence's two statements are true simultaneously. It is the point at which the solution sets for the various statements overlap or intersect.
¶A type of inequality with two or more parts is a compound inequality. These components may be "or" or "and" statements. If your inequality reads, "x is greater than 5 and less than 10," for instance, x could be any number between 5 and 10.
If a man goes 15 m due north and then 8 m due east, then his distance from the starting point is ……..
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Write a compound inequality for each graph:
Write a compound inequality for each graph:
Consider the solutions of the compound inequalities.
4 < x < 8 2 < x < 11
Describe each solution as a set. Is one set a subset of the other? Explain your answer.
A compound inequality is a sentence that contains two inequality statements separated by the words "or" or "and." The term "and" indicates that both of the compound sentence's statements are true simultaneously. The intersection of the solutions of two inequalities joined by the word and the solution of a compound inequality. All of the solutions having the two inequalities in common are the solutions to a compound inequality, where the two graphs overlap, as we saw in the previous sections.
¶The graph of a compound inequality with a "and" denotes the intersection of the inequalities' graphs. If a number solves both inequalities, it solves the compound inequality. It can be written as x > -1 and x < 2 or as -1 < x < 2.
¶Graph the compound inequality x > 1 AND x ≤ 4.
Consider the solutions of the compound inequalities.
4 < x < 8 2 < x < 11
Describe each solution as a set. Is one set a subset of the other? Explain your answer.
A compound inequality is a sentence that contains two inequality statements separated by the words "or" or "and." The term "and" indicates that both of the compound sentence's statements are true simultaneously. The intersection of the solutions of two inequalities joined by the word and the solution of a compound inequality. All of the solutions having the two inequalities in common are the solutions to a compound inequality, where the two graphs overlap, as we saw in the previous sections.
¶The graph of a compound inequality with a "and" denotes the intersection of the inequalities' graphs. If a number solves both inequalities, it solves the compound inequality. It can be written as x > -1 and x < 2 or as -1 < x < 2.
¶Graph the compound inequality x > 1 AND x ≤ 4.
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When the two expressions are not equal and related to each other, known as inequality. They are denoted by a sign like ≠ “not equal to,” > “greater than,” or < “less than.”.
If a and b have polynomial equations, then there will be a curve between a and b:
- [ b < x < a ]
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b < x < a
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
When the two expressions are not equal and related to each other, known as inequality. They are denoted by a sign like ≠ “not equal to,” > “greater than,” or < “less than.”.
If a and b have polynomial equations, then there will be a curve between a and b:
- [ b < x < a ]
It will be a line between a and b x > a and x < b if the equations for a and b are linear.
b < x < a
