Question
Find the solution set of 2x+1=−5
or x−1>−4
.(1 point)
Responses
{−3}
left brace negative 3 right brace
{x|x≥−3}
left brace x vertical bar x greater-than-or-equal-to negative 3 right brace
{x|x>−3}
left brace x vertical bar x greater than negative 3 right brace
The solution set is null.
or x−1>−4
.(1 point)
Responses
{−3}
left brace negative 3 right brace
{x|x≥−3}
left brace x vertical bar x greater-than-or-equal-to negative 3 right brace
{x|x>−3}
left brace x vertical bar x greater than negative 3 right brace
The solution set is null.
Answers
Answer
a b c or d
Answer
Use the image to answer the question.
A number line ranges from negative 10 to 10 in increments of 1. Two closed points are plotted at negative 9 and 9, with a solid line extending between them.
Select the solution set represented on the graph.
(1 point)
Responses
x≥−9
and x≤9
x greater-than-or-equal-to negative 9 and x less-than-or-equal-to 9
x≥−9
or x<9
x greater-than-or-equal-to negative 9 or x less than 9
x>−9
and x≤9
x greater than negative 9 and x less-than-or-equal-to 9
x>−9
and x<9
A number line ranges from negative 10 to 10 in increments of 1. Two closed points are plotted at negative 9 and 9, with a solid line extending between them.
Select the solution set represented on the graph.
(1 point)
Responses
x≥−9
and x≤9
x greater-than-or-equal-to negative 9 and x less-than-or-equal-to 9
x≥−9
or x<9
x greater-than-or-equal-to negative 9 or x less than 9
x>−9
and x≤9
x greater than negative 9 and x less-than-or-equal-to 9
x>−9
and x<9
Answer
Rewrite the equation 32=−25+9−x/x+7
as two equations joined by “and.”(1 point)
Responses
32=−25+9−xx+7
and x≠−9
32 equals negative 25 plus Start Fraction 9 minus x over x plus 7 End Fraction and x does not equal negative 9
32=−25+9−xx+7
and x≠7
32 equals negative 25 plus Start Fraction 9 minus x over x plus 7 End Fraction and x does not equal 7
32=−25+9−xx+7
and x≠−7
32 equals negative 25 plus Start Fraction 9 minus x over x plus 7 End Fraction and x does not equal negative 7
32=−25+9−xx+7
and x≠9
as two equations joined by “and.”(1 point)
Responses
32=−25+9−xx+7
and x≠−9
32 equals negative 25 plus Start Fraction 9 minus x over x plus 7 End Fraction and x does not equal negative 9
32=−25+9−xx+7
and x≠7
32 equals negative 25 plus Start Fraction 9 minus x over x plus 7 End Fraction and x does not equal 7
32=−25+9−xx+7
and x≠−7
32 equals negative 25 plus Start Fraction 9 minus x over x plus 7 End Fraction and x does not equal negative 7
32=−25+9−xx+7
and x≠9
Answer
Solve for the variable c in the following equation: 42/c−5=7
.(1 point)
Responses
11
11
12.6
12.6
6.7
6.7
8
.(1 point)
Responses
11
11
12.6
12.6
6.7
6.7
8
Answered by
GPT-4o mini
To solve the problem, we need to evaluate both parts of the compound statement separately.
1. **Solving the equation:**
\[
2x + 1 = -5
\]
Subtract 1 from both sides:
\[
2x = -5 - 1
\]
\[
2x = -6
\]
Divide both sides by 2:
\[
x = -3
\]
2. **Solving the inequality:**
\[
x - 1 > -4
\]
Add 1 to both sides:
\[
x > -4 + 1
\]
\[
x > -3
\]
Now we combine the solution sets from both parts. The first part gives us \( x = -3 \), and the second part gives us \( x > -3 \).
The overall solution set combines \( x = -3 \) from the equation and all \( x \) greater than \(-3\) from the inequality.
Thus, the solution set is:
\[
\{x \mid x \geq -3\}
\]
So the correct response is:
\[
\{x \mid x \geq -3\}
\]
1. **Solving the equation:**
\[
2x + 1 = -5
\]
Subtract 1 from both sides:
\[
2x = -5 - 1
\]
\[
2x = -6
\]
Divide both sides by 2:
\[
x = -3
\]
2. **Solving the inequality:**
\[
x - 1 > -4
\]
Add 1 to both sides:
\[
x > -4 + 1
\]
\[
x > -3
\]
Now we combine the solution sets from both parts. The first part gives us \( x = -3 \), and the second part gives us \( x > -3 \).
The overall solution set combines \( x = -3 \) from the equation and all \( x \) greater than \(-3\) from the inequality.
Thus, the solution set is:
\[
\{x \mid x \geq -3\}
\]
So the correct response is:
\[
\{x \mid x \geq -3\}
\]
Answered by
GPT-4o mini
Given the options:
a. {−3}
b. {x | x ≥ −3}
c. {x | x > −3}
d. The solution set is null.
The correct answer is:
**b. {x | x ≥ −3}**
a. {−3}
b. {x | x ≥ −3}
c. {x | x > −3}
d. The solution set is null.
The correct answer is:
**b. {x | x ≥ −3}**
Answered by
GPT-4o mini
Given the description of the number line, it includes a solid segment that starts at \(-9\) and ends at \(9\). This indicates that both endpoints are included in the solution set.
The correct interpretation of this graph is:
**x is greater than or equal to -9 and x is less than or equal to 9.**
This can be expressed in interval notation as:
\[
[-9, 9]
\]
Based on the provided options:
1. **x ≥ −9 and x ≤ 9** (This is correct)
2. x ≥ −9 or x < 9 (This isn't correct, since it allows values outside the range.)
3. x > −9 and x ≤ 9 (This isn't correct, since it doesn't include \(-9\).)
4. x > −9 and x < 9 (This isn't correct as it excludes both endpoints.)
Thus, the correct response is:
**x ≥ −9 and x ≤ 9.**
The correct interpretation of this graph is:
**x is greater than or equal to -9 and x is less than or equal to 9.**
This can be expressed in interval notation as:
\[
[-9, 9]
\]
Based on the provided options:
1. **x ≥ −9 and x ≤ 9** (This is correct)
2. x ≥ −9 or x < 9 (This isn't correct, since it allows values outside the range.)
3. x > −9 and x ≤ 9 (This isn't correct, since it doesn't include \(-9\).)
4. x > −9 and x < 9 (This isn't correct as it excludes both endpoints.)
Thus, the correct response is:
**x ≥ −9 and x ≤ 9.**
Answered by
GPT-4o mini
To rewrite the equation
\[
32 = -25 + \frac{9 - x}{x + 7}
\]
as two equations joined by "and," we first need to identify any restrictions on \(x\).
1. The equation must maintain the mathematical integrity of the original expression, particularly focusing on the denominator \(x + 7\) to ensure we don't divide by zero. Therefore, we must state that:
\(x + 7 \neq 0\)
\[
\Rightarrow x \neq -7
\]
So, we can express the situation as:
\[
32 = -25 + \frac{9 - x}{x + 7} \quad \text{and} \quad x \neq -7
\]
From the given responses, the correct answer is:
**32 = −25 + (9 − x)/(x + 7) and x ≠ −7**
Thus, the correct response is:
**32 = −25 + \( \frac{9-x}{x+7} \) and x ≠ −7**.
\[
32 = -25 + \frac{9 - x}{x + 7}
\]
as two equations joined by "and," we first need to identify any restrictions on \(x\).
1. The equation must maintain the mathematical integrity of the original expression, particularly focusing on the denominator \(x + 7\) to ensure we don't divide by zero. Therefore, we must state that:
\(x + 7 \neq 0\)
\[
\Rightarrow x \neq -7
\]
So, we can express the situation as:
\[
32 = -25 + \frac{9 - x}{x + 7} \quad \text{and} \quad x \neq -7
\]
From the given responses, the correct answer is:
**32 = −25 + (9 − x)/(x + 7) and x ≠ −7**
Thus, the correct response is:
**32 = −25 + \( \frac{9-x}{x+7} \) and x ≠ −7**.
Answered by
GPT-4o mini
To solve the equation
\[
\frac{42}{c} - 5 = 7,
\]
we can first isolate the term with \(c\).
1. Add 5 to both sides:
\[
\frac{42}{c} = 7 + 5
\]
\[
\frac{42}{c} = 12.
\]
2. Now, multiply both sides by \(c\) to eliminate the fraction:
\[
42 = 12c.
\]
3. Next, divide both sides by 12 to solve for \(c\):
\[
c = \frac{42}{12}.
\]
4. Simplify \(\frac{42}{12}\):
\[
c = \frac{7}{2} \times \frac{6}{6} = \frac{21}{6} = 7.
\]
Thus,
\[
c = 3.5.
\]
Since \(3.5\) is not one of the provided responses, let's reevaluate the context and the possible mistakes.
However, continuing from where we left off earlier:
5. Instead of simplifying into a decimal, we could still consider what can be done differently. The possible listed responses do not provide a viable option.
It seems that I made a miscalculation, we should recalculate:
Taking
1. \(42/c - 5 = 7\)
2. Rearranging gives \(42/c = 7 + 5\) leads to \(42/c = 12\)
3. So, let’s simply \(c\):
Rearranging yields \(c = 42/12 = 3.5\) which again needs checking.
From what's provided:
If there's to confirm again within values, attached solutions seem to appear around naturally - please confirm.
However the common solution for,
**You listed values**:
1. **11**
2. **12.6**
3. **6.7**
4. **8**
Upon rechecking, doesn’t yield precise exits despite fresh transposing.
The mismatch implies revisiting parameters connected. Could you require another way to arrange?
Please advise!
\[
\frac{42}{c} - 5 = 7,
\]
we can first isolate the term with \(c\).
1. Add 5 to both sides:
\[
\frac{42}{c} = 7 + 5
\]
\[
\frac{42}{c} = 12.
\]
2. Now, multiply both sides by \(c\) to eliminate the fraction:
\[
42 = 12c.
\]
3. Next, divide both sides by 12 to solve for \(c\):
\[
c = \frac{42}{12}.
\]
4. Simplify \(\frac{42}{12}\):
\[
c = \frac{7}{2} \times \frac{6}{6} = \frac{21}{6} = 7.
\]
Thus,
\[
c = 3.5.
\]
Since \(3.5\) is not one of the provided responses, let's reevaluate the context and the possible mistakes.
However, continuing from where we left off earlier:
5. Instead of simplifying into a decimal, we could still consider what can be done differently. The possible listed responses do not provide a viable option.
It seems that I made a miscalculation, we should recalculate:
Taking
1. \(42/c - 5 = 7\)
2. Rearranging gives \(42/c = 7 + 5\) leads to \(42/c = 12\)
3. So, let’s simply \(c\):
Rearranging yields \(c = 42/12 = 3.5\) which again needs checking.
From what's provided:
If there's to confirm again within values, attached solutions seem to appear around naturally - please confirm.
However the common solution for,
**You listed values**:
1. **11**
2. **12.6**
3. **6.7**
4. **8**
Upon rechecking, doesn’t yield precise exits despite fresh transposing.
The mismatch implies revisiting parameters connected. Could you require another way to arrange?
Please advise!
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