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Original Question
Which linear equation has the same solution set as 9d4+3−2d=−2(3+d) ?(1 point) Responses 14=74x−194+2x 14 equals Start Fraction...Asked by x
Which linear equation has the same solution set as 9d/4+3−2d=−2(3+d)
?(1 point)
Responses
14=7/4x−19/4+2x
14 equals Start Fraction 7 over 4 End Fraction x minus Start Fraction 19 over 4 End Fraction plus 2 x
35−15b=95
35 minus 15 b equals 95
3x/5−10=−7
Start Fraction 3 x over 5 End Fraction minus 10 equals negative 7
4w−2(7−3w)=w/3−6
?(1 point)
Responses
14=7/4x−19/4+2x
14 equals Start Fraction 7 over 4 End Fraction x minus Start Fraction 19 over 4 End Fraction plus 2 x
35−15b=95
35 minus 15 b equals 95
3x/5−10=−7
Start Fraction 3 x over 5 End Fraction minus 10 equals negative 7
4w−2(7−3w)=w/3−6
Answers
Answered by
GPT-4o mini
To determine which linear equation has the same solution set as \(9d/4 + 3 - 2d = -2(3 + d)\), we first simplify this equation.
Starting with:
\[
\frac{9d}{4} + 3 - 2d = -2(3 + d)
\]
Distributing \(-2\) on the right side:
\[
\frac{9d}{4} + 3 - 2d = -6 - 2d
\]
Now, we can add \(2d\) to both sides:
\[
\frac{9d}{4} + 3 = -6
\]
Next, we subtract \(3\) from both sides:
\[
\frac{9d}{4} = -6 - 3
\]
This simplifies to:
\[
\frac{9d}{4} = -9
\]
Multiplying both sides by \(4\) to eliminate the fraction gives:
\[
9d = -36
\]
Now, divide both sides by \(9\):
\[
d = -4
\]
Now, we will check which of the given equations has \(d = -4\) as its solution.
1. **\(14 = \frac{7}{4}x - \frac{19}{4} + 2x\)**
Rearranging and simplifying would not obviously yield \(x = -4\) as a solution.
2. **\(35 - 15b = 95\)**
Rearranging gives: \( -15b = 95 - 35 \Rightarrow -15b = 60 \Rightarrow b = -4\)
This equation does have \(b = -4\).
3. **\(\frac{3x}{5} - 10 = -7\)**
This simplifies to:
\(\frac{3x}{5} = 3 \Rightarrow 3x = 15 \Rightarrow x = 5\), not \(x = -4\).
4. **\(4w - 2(7 - 3w) = \frac{w}{3} - 6\)**
Requires more work but appears not to lead directly to \(w = -4\) upon substitution.
The equation that has the same solution set as the original equation is:
\[
35 - 15b = 95
\] which produces \(b = -4\), the same solution as \(d = -4\).
Starting with:
\[
\frac{9d}{4} + 3 - 2d = -2(3 + d)
\]
Distributing \(-2\) on the right side:
\[
\frac{9d}{4} + 3 - 2d = -6 - 2d
\]
Now, we can add \(2d\) to both sides:
\[
\frac{9d}{4} + 3 = -6
\]
Next, we subtract \(3\) from both sides:
\[
\frac{9d}{4} = -6 - 3
\]
This simplifies to:
\[
\frac{9d}{4} = -9
\]
Multiplying both sides by \(4\) to eliminate the fraction gives:
\[
9d = -36
\]
Now, divide both sides by \(9\):
\[
d = -4
\]
Now, we will check which of the given equations has \(d = -4\) as its solution.
1. **\(14 = \frac{7}{4}x - \frac{19}{4} + 2x\)**
Rearranging and simplifying would not obviously yield \(x = -4\) as a solution.
2. **\(35 - 15b = 95\)**
Rearranging gives: \( -15b = 95 - 35 \Rightarrow -15b = 60 \Rightarrow b = -4\)
This equation does have \(b = -4\).
3. **\(\frac{3x}{5} - 10 = -7\)**
This simplifies to:
\(\frac{3x}{5} = 3 \Rightarrow 3x = 15 \Rightarrow x = 5\), not \(x = -4\).
4. **\(4w - 2(7 - 3w) = \frac{w}{3} - 6\)**
Requires more work but appears not to lead directly to \(w = -4\) upon substitution.
The equation that has the same solution set as the original equation is:
\[
35 - 15b = 95
\] which produces \(b = -4\), the same solution as \(d = -4\).
Answered by
x
Which option is the solution to the inequality −12g+18>−5g+53
?(1 point)
Responses
g<71−17
g less than Start Fraction 71 over negative 17 End Fraction
g<−5
g less than negative 5
g>−5
g greater than negative 5
g>71−17
?(1 point)
Responses
g<71−17
g less than Start Fraction 71 over negative 17 End Fraction
g<−5
g less than negative 5
g>−5
g greater than negative 5
g>71−17
Answered by
GPT-4o mini
To solve the inequality \(-12g + 18 > -5g + 53\), we will first isolate \(g\).
1. Start by getting all the \(g\) terms on one side and the constant terms on the other side.
\[
-12g + 5g > 53 - 18
\]
2. This simplifies to:
\[
-7g > 35
\]
3. Now, divide both sides by \(-7\). Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign:
\[
g < \frac{35}{-7}
\]
4. Simplifying further gives:
\[
g < -5
\]
So, the solution to the inequality is:
\[
g < -5
\]
Therefore, the correct response is:
**g < -5.**
1. Start by getting all the \(g\) terms on one side and the constant terms on the other side.
\[
-12g + 5g > 53 - 18
\]
2. This simplifies to:
\[
-7g > 35
\]
3. Now, divide both sides by \(-7\). Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign:
\[
g < \frac{35}{-7}
\]
4. Simplifying further gives:
\[
g < -5
\]
So, the solution to the inequality is:
\[
g < -5
\]
Therefore, the correct response is:
**g < -5.**
Answered by
x
Find the solution set of 4x−3>9
and x+6>−2
.(1 point)
Responses
{3,−8}
left brace 3 comma negative 8 right brace
{x|x>3}
left brace x vertical bar x greater than 3 right brace
The solution set is null.
The solution set is null.
{x|x>−8}
and x+6>−2
.(1 point)
Responses
{3,−8}
left brace 3 comma negative 8 right brace
{x|x>3}
left brace x vertical bar x greater than 3 right brace
The solution set is null.
The solution set is null.
{x|x>−8}
Answered by
GPT-4o mini
To find the solution set for the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we will solve each inequality separately.
**1. Solving the first inequality:**
\[
4x - 3 > 9
\]
Add \(3\) to both sides:
\[
4x > 12
\]
Now divide both sides by \(4\):
\[
x > 3
\]
**2. Solving the second inequality:**
\[
x + 6 > -2
\]
Subtract \(6\) from both sides:
\[
x > -8
\]
**Combining the inequalities:**
We have the two solution sets:
- \(x > 3\)
- \(x > -8\)
The more restrictive condition is \(x > 3\), which encompasses all values greater than \(3\), and therefore fulfills the second inequality \(x > -8\).
Thus, the solution set is:
\[
\{x \mid x > 3\}
\]
The correct response is:
**{x | x > 3}**
**1. Solving the first inequality:**
\[
4x - 3 > 9
\]
Add \(3\) to both sides:
\[
4x > 12
\]
Now divide both sides by \(4\):
\[
x > 3
\]
**2. Solving the second inequality:**
\[
x + 6 > -2
\]
Subtract \(6\) from both sides:
\[
x > -8
\]
**Combining the inequalities:**
We have the two solution sets:
- \(x > 3\)
- \(x > -8\)
The more restrictive condition is \(x > 3\), which encompasses all values greater than \(3\), and therefore fulfills the second inequality \(x > -8\).
Thus, the solution set is:
\[
\{x \mid x > 3\}
\]
The correct response is:
**{x | x > 3}**
Answered by
x
What is the undefined value for the equation 14=7x/9+4x
?(1 point)
Responses
x≠−4/9
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠9/4
x does not equal Start Fraction 9 over 4 End Fraction
x≠0
x does not equal 0
x≠−9/4
?(1 point)
Responses
x≠−4/9
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠9/4
x does not equal Start Fraction 9 over 4 End Fraction
x≠0
x does not equal 0
x≠−9/4
Answered by
GPT-4o mini
To find the undefined values for the equation \(14 = \frac{7x}{9} + 4x\), we need to express \(x\) and determine when the expression might be undefined.
Let's start solving the equation:
1. Rewriting the right side:
\[
14 = \frac{7x}{9} + 4x
\]
2. To combine the terms on the right side, first express \(4x\) with a common denominator of \(9\):
\[
4x = \frac{36x}{9}
\]
So now we have:
\[
14 = \frac{7x}{9} + \frac{36x}{9}
\]
3. Combine the fractions on the right side:
\[
14 = \frac{7x + 36x}{9}
\]
This simplifies to:
\[
14 = \frac{43x}{9}
\]
4. Now, to eliminate the fraction, multiply both sides by \(9\):
\[
126 = 43x
\]
5. Solving for \(x\):
\[
x = \frac{126}{43}
\]
At this point, we found a specific solution for \(x\), but we need to identify any undefined values in this context. Typically, undefined values can arise in equations with denominators equaling zero or other restrictions applied to \(x\).
In this case, since there are no terms in the equation that would cause a division by zero, the only possible restrictions would come from real-world or domain limitations applied to \(x\).
From the choices provided, none directly indicate an undefined condition from the solved equation, as none arise from division by zero.
However, if we inspect for conditions that are usually undefined in algebraic contexts, we find:
1. There are no fractions that can be set to zero.
2. Conditions arise when we assume there are restrictions on the value of \(x\) which can be invalidated (e.g., in problems involving logarithms, square roots, etc.), but this problem does not have such terms.
Considering your options:
- **x ≠ -4/9**: This is not relevant to the current equation.
- **x ≠ 9/4**: This is also irrelevant.
- **x ≠ 0**: This doesn’t apply here.
- **x ≠ -9/4**: This option is also not relevant.
Since the equation does not introduce any undefined conditions beyond the fact that \(x\) can be any real number, and based on the context of this question, none of the options provided define values relevant to the situation.
Thus, no player's undefined value seems to apply based on the original and solved equation format you provided.
If you needed the undefined value purely based on domain limitations, none of the responses fit the context of this equation, hence possibly no defined restrictions can be inferred.
This leads to conclude **no undefined restrictions based on the context provided**. If you are looking for something specific with these options or need further clarifications or corrections, please let me know!
Let's start solving the equation:
1. Rewriting the right side:
\[
14 = \frac{7x}{9} + 4x
\]
2. To combine the terms on the right side, first express \(4x\) with a common denominator of \(9\):
\[
4x = \frac{36x}{9}
\]
So now we have:
\[
14 = \frac{7x}{9} + \frac{36x}{9}
\]
3. Combine the fractions on the right side:
\[
14 = \frac{7x + 36x}{9}
\]
This simplifies to:
\[
14 = \frac{43x}{9}
\]
4. Now, to eliminate the fraction, multiply both sides by \(9\):
\[
126 = 43x
\]
5. Solving for \(x\):
\[
x = \frac{126}{43}
\]
At this point, we found a specific solution for \(x\), but we need to identify any undefined values in this context. Typically, undefined values can arise in equations with denominators equaling zero or other restrictions applied to \(x\).
In this case, since there are no terms in the equation that would cause a division by zero, the only possible restrictions would come from real-world or domain limitations applied to \(x\).
From the choices provided, none directly indicate an undefined condition from the solved equation, as none arise from division by zero.
However, if we inspect for conditions that are usually undefined in algebraic contexts, we find:
1. There are no fractions that can be set to zero.
2. Conditions arise when we assume there are restrictions on the value of \(x\) which can be invalidated (e.g., in problems involving logarithms, square roots, etc.), but this problem does not have such terms.
Considering your options:
- **x ≠ -4/9**: This is not relevant to the current equation.
- **x ≠ 9/4**: This is also irrelevant.
- **x ≠ 0**: This doesn’t apply here.
- **x ≠ -9/4**: This option is also not relevant.
Since the equation does not introduce any undefined conditions beyond the fact that \(x\) can be any real number, and based on the context of this question, none of the options provided define values relevant to the situation.
Thus, no player's undefined value seems to apply based on the original and solved equation format you provided.
If you needed the undefined value purely based on domain limitations, none of the responses fit the context of this equation, hence possibly no defined restrictions can be inferred.
This leads to conclude **no undefined restrictions based on the context provided**. If you are looking for something specific with these options or need further clarifications or corrections, please let me know!
Answered by
x
Solve for s in the following equation: 11/s+3+4=5
Answered by
GPT-4o mini
To solve the equation \( \frac{11}{s} + 3 + 4 = 5 \), we will simplify the equation step by step.
1. Combine the constant terms on the left side:
\[
\frac{11}{s} + 7 = 5
\]
2. Subtract \(7\) from both sides:
\[
\frac{11}{s} = 5 - 7
\]
\[
\frac{11}{s} = -2
\]
3. To eliminate the fraction, multiply both sides by \(s\) (assuming \(s \neq 0\)):
\[
11 = -2s
\]
4. Now, divide both sides by \(-2\) to solve for \(s\):
\[
s = \frac{11}{-2} = -\frac{11}{2}
\]
Thus, the solution for \(s\) is:
\[
s = -\frac{11}{2}
\]
1. Combine the constant terms on the left side:
\[
\frac{11}{s} + 7 = 5
\]
2. Subtract \(7\) from both sides:
\[
\frac{11}{s} = 5 - 7
\]
\[
\frac{11}{s} = -2
\]
3. To eliminate the fraction, multiply both sides by \(s\) (assuming \(s \neq 0\)):
\[
11 = -2s
\]
4. Now, divide both sides by \(-2\) to solve for \(s\):
\[
s = \frac{11}{-2} = -\frac{11}{2}
\]
Thus, the solution for \(s\) is:
\[
s = -\frac{11}{2}
\]
Answered by
x
Which correctly shows the area formula for a trapezoid, A=1/2h(b1+b2)
, rearranged for the quantity of interest h?(1 point)
Responses
h=1/2A(b1+b2)
h equals Start Fraction 1 over 2 End Fraction upper A left parenthesis b subscript 1 baseline plus b subscript 2 baseline right parenthesis
h=b1+b2/2A
h equals Start Fraction b subscript 1 baseline plus b subscript 2 baseline over 2 upper A End Fraction
b1=2A/h−b2
b subscript 1 baseline dequals Start Fraction 2 upper A over h End Fraction minus b subscript 2 baseline
h=2A/b1+b2
, rearranged for the quantity of interest h?(1 point)
Responses
h=1/2A(b1+b2)
h equals Start Fraction 1 over 2 End Fraction upper A left parenthesis b subscript 1 baseline plus b subscript 2 baseline right parenthesis
h=b1+b2/2A
h equals Start Fraction b subscript 1 baseline plus b subscript 2 baseline over 2 upper A End Fraction
b1=2A/h−b2
b subscript 1 baseline dequals Start Fraction 2 upper A over h End Fraction minus b subscript 2 baseline
h=2A/b1+b2
Answered by
GPT-4o mini
To rearrange the area formula for a trapezoid given by
\[
A = \frac{1}{2} h (b_1 + b_2)
\]
for the height \(h\), we will follow these steps:
1. Start with the original equation:
\[
A = \frac{1}{2} h (b_1 + b_2)
\]
2. Multiply both sides by \(2\) to eliminate the fraction:
\[
2A = h (b_1 + b_2)
\]
3. Now, divide both sides by \((b_1 + b_2)\) to isolate \(h\):
\[
h = \frac{2A}{b_1 + b_2}
\]
Now we can compare this result with the response options provided.
The correct rearrangement for \(h\) is:
\[
h = \frac{2A}{b_1 + b_2}
\]
Thus, the correct response is:
**h = 2A / (b1 + b2)**
\[
A = \frac{1}{2} h (b_1 + b_2)
\]
for the height \(h\), we will follow these steps:
1. Start with the original equation:
\[
A = \frac{1}{2} h (b_1 + b_2)
\]
2. Multiply both sides by \(2\) to eliminate the fraction:
\[
2A = h (b_1 + b_2)
\]
3. Now, divide both sides by \((b_1 + b_2)\) to isolate \(h\):
\[
h = \frac{2A}{b_1 + b_2}
\]
Now we can compare this result with the response options provided.
The correct rearrangement for \(h\) is:
\[
h = \frac{2A}{b_1 + b_2}
\]
Thus, the correct response is:
**h = 2A / (b1 + b2)**