Question
Solve 3(2x-5) >15 and 4(2x-1) >10
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 final inequality is x > 5.
Solving the first inequality for x
3(2x-5) >1
Dividing 3 both sides
2x - 5 > 5
2x > 10
Dividing 2 both sides
x > 5
Solving the second inequality for x
4(2x-1) >10
Dividing 4 both sides
2x-1 > 2.5
2x > 3.5
Dividing 2 both sides
x > 1.75
So, the final result is x > 5 and x > 1.75
Plotting the graph
Final Answer:
Hence, the final inequality is x > 5.
Dividing 3 both sides
Dividing 2 both sides
Solving the second inequality for x
Dividing 4 both sides
Dividing 2 both sides
So, the final result is x > 5 and x > 1.75
Plotting the graph
Final Answer:
Hence, the final inequality is x > 5.
Related Questions to study
A 2.5m long ladder leans against the wall of a building. The base of the ladder is 1.5m away from the wall. What is the height of the wall?
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Solve 0.5x-5 > -3 or +4 < 3 , graph the solution
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Solve x-6 ≤ 18 and 3-2x ≥ 11, and graph the solution.
Write a compound inequality for each graph:
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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.
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 ……..
If a man goes 15 m due north and then 8 m due east, then his distance from the starting point is ……..
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.
Describe and correct the error a student made graphing the compound inequality x>3 or x <-1
Describe and correct the error a student made graphing the compound inequality x>3 or x <-1
Solve -24 < 4x-4 < 4. Graph the solution.
Solve -24 < 4x-4 < 4. Graph the solution.
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
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
