Question
Solve the compound inequality -3x + 2 > -7 or 2(x - 2) ≥ 6. Graph the solution:
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: the final inequality is x < 3 or x ≥ 5.
Solving the first inequality for x
-3x + 2 > -7
-3x > -9
Dividing -3 both sides
x < 3
Solving the second inequality for x
2 (x - 2) ≥ 6
Dividing 2 both sides
x - 2 ≥ 3
x ≥ 5
So, the final result is x < 3 or x ≥ 5
Plotting the graph
Final Answer:
Hence, the final inequality is x < 3 or x ≥ 5.
Dividing -3 both sides
Solving the second inequality for x
Dividing 2 both sides
So, the final result is x < 3 or x ≥ 5
Plotting the graph
Final Answer:
Hence, the final inequality is x < 3 or x ≥ 5.
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.
Related Questions to study
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Solve the compound inequality 5x+7 < 13 or -4x+3 > 11. Graph the solution.
A Compound inequality is a connection between two inequality statements by the words "or" or "and." The conjunction "and" denotes the simultaneous truth of both statements in a compound sentence. It is the point where the solution sets for the various statements cross over or intersect. The conjunction "or" denotes that the entire compound sentence is true as long as either of the two statements is true — the union or combination of the solution sets for each particular statement.
Let's see x: 2 x + 7 < –11 or –3 x – 2 < 13. Solve each inequality on its own. Combine the solutions, i.e., determine the union of the solution sets for each inequality phrase since the connecting word is "or." Both x < –9 and x > -5 denote all the numbers on the left of those two particular values. Written as follows is the solution set:
{ x| x < -9 or x > -5}
Solve the compound inequality 5x+7 < 13 or -4x+3 > 11. Graph the solution.
A Compound inequality is a connection between two inequality statements by the words "or" or "and." The conjunction "and" denotes the simultaneous truth of both statements in a compound sentence. It is the point where the solution sets for the various statements cross over or intersect. The conjunction "or" denotes that the entire compound sentence is true as long as either of the two statements is true — the union or combination of the solution sets for each particular statement.
Let's see x: 2 x + 7 < –11 or –3 x – 2 < 13. Solve each inequality on its own. Combine the solutions, i.e., determine the union of the solution sets for each inequality phrase since the connecting word is "or." Both x < –9 and x > -5 denote all the numbers on the left of those two particular values. Written as follows is the solution set:
{ x| x < -9 or x > -5}
