Question
Solve the compound inequality: -12 ≤ 7x + 9 < 16 and 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.
The correct answer is: the final inequality is -3 ≤ x < 1
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.
-12 ≤ 7x + 9 < 16
Subtracting 9 on all sides
-12 - 9 ≤ 7x < 16 - 9
-21 ≤ 7x < 7
Dividing 7 on all sides
-3 ≤ x < 1
Plotting the graph
Final Answer:
Hence, the final inequality is -3 ≤ x < 1
Subtracting 9 on all sides
Dividing 7 on all sides
Plotting the graph
Final Answer:
Hence, the final inequality is -3 ≤ x < 1
Related Questions to study
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Observe the diagram carefully and find x and y.
Observe the given window and explain which lines are parallel.
Observe the given window and explain which lines are parallel.
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Ajit is 21 years younger than his father. What is their total age in 7 years' time?
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Solve each compound inequality and graph the solution.
2x+5 > -3 and 4x+7 < 15
When two inequality statements are joined by the words "or" or "and," the sentence is said to be compound inequality. The preposition "and" denotes that both statements in the compound sentence are true simultaneously. It is where the solution sets for the several statements to cross or overlap. The conjunction "or" indicates that the whole compound statement is true.
Example
Solve for x: 3 x + 2 < 14 and 2 x – 5 > –11
Here we have to solve each inequality individually. Because the joining word is "and," the overlap or intersection is the desired outcome.
3x+2<14 and 2x-5>-11
3x<12 2x>-6
x<4 x>-3
Numbers to the left of 4 are represented by x < 4, and the right of -3 is represented by x > -3. The solution set consists of {x| x > –3 and x < 4}
Solve each compound inequality and graph the solution.
2x+5 > -3 and 4x+7 < 15
When two inequality statements are joined by the words "or" or "and," the sentence is said to be compound inequality. The preposition "and" denotes that both statements in the compound sentence are true simultaneously. It is where the solution sets for the several statements to cross or overlap. The conjunction "or" indicates that the whole compound statement is true.
Example
Solve for x: 3 x + 2 < 14 and 2 x – 5 > –11
Here we have to solve each inequality individually. Because the joining word is "and," the overlap or intersection is the desired outcome.
3x+2<14 and 2x-5>-11
3x<12 2x>-6
x<4 x>-3
Numbers to the left of 4 are represented by x < 4, and the right of -3 is represented by x > -3. The solution set consists of {x| x > –3 and x < 4}
Solve the compound inequality -3x + 2 > -7 or 2(x - 2) ≥ 6. Graph the solution:
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.
Solve the compound inequality -3x + 2 > -7 or 2(x - 2) ≥ 6. Graph the solution:
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.
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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}
