Question
What is the solution of the equation x + 24 = −17
?(1 point)
Responses
7
7
−7
negative 7
41
41
−41
?(1 point)
Responses
7
7
−7
negative 7
41
41
−41
Answers
Answer
Which of the following equations has the same solution as the equation x + 1/2 = −1/4
?(1 point)
Responses
x + 1.5 = 0.75
x plus 1.5 equals 0.75
x − 0.70 = −0.05
x minus 0.70 equals negative 0.05
x − 1/4 = 1
x minus Start Fraction 1 over 4 End Fraction equals 1
x + 1/2 = 5/4
?(1 point)
Responses
x + 1.5 = 0.75
x plus 1.5 equals 0.75
x − 0.70 = −0.05
x minus 0.70 equals negative 0.05
x − 1/4 = 1
x minus Start Fraction 1 over 4 End Fraction equals 1
x + 1/2 = 5/4
Answer
i dont understand
simplify
simplify
Answered by
GPT-4o mini
To solve the equation \( x + 24 = -17 \), you can isolate \( x \) by subtracting 24 from both sides:
\[
x + 24 - 24 = -17 - 24
\]
This simplifies to:
\[
x = -41
\]
So, the solution to the equation is \( -41 \).
\[
x + 24 - 24 = -17 - 24
\]
This simplifies to:
\[
x = -41
\]
So, the solution to the equation is \( -41 \).
Answered by
GPT-4o mini
To determine which equation has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \), we first need to solve the original equation for \( x \):
\[
x + \frac{1}{2} = -\frac{1}{4}
\]
Subtract \( \frac{1}{2} \) from both sides:
\[
x = -\frac{1}{4} - \frac{1}{2}
\]
To perform the subtraction, we convert \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[
-\frac{1}{4} - \frac{2}{4} = -\frac{3}{4}
\]
So, the solution for the equation \( x + \frac{1}{2} = -\frac{1}{4} \) is \( x = -\frac{3}{4} \).
Now, we will check each option to see which one also yields \( x = -\frac{3}{4} \).
1. **Option 1:** \( x + 1.5 = 0.75 \)
\[
x = 0.75 - 1.5 = -0.75
\]
(Not equal to \(-\frac{3}{4}\))
2. **Option 2:** \( x - 0.70 = -0.05 \)
\[
x = -0.05 + 0.70 = 0.65
\]
(Not equal to \(-\frac{3}{4}\))
3. **Option 3:** \( x - \frac{1}{4} = 1 \)
\[
x = 1 + \frac{1}{4} = 1.25
\]
(Not equal to \(-\frac{3}{4}\))
4. **Option 4:** \( x + \frac{1}{2} = \frac{5}{4} \)
\[
x = \frac{5}{4} - \frac{1}{2}
\]
Converting \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[
x = \frac{5}{4} - \frac{2}{4} = \frac{3}{4}
\]
(Not equal to \(-\frac{3}{4}\))
None of the equations seem to yield \( x = -\frac{3}{4} \), which is surprising. However, upon closely checking for a correct equivalency:
Let's find a connection:
The equation \( x + 1/2 = −1/4 \) can also be transformed linearly into something comparable to the options.
To find an equivalent equation, reconsider the manipulation or transformations of constants. For matching forms or rearrangements in other equations to determine correctness.
The first key check leads to a review focusing especially how negatives change entries.
As none of the derived solutions match the problem scope precisely as conceptualized from the initial equation.
It seems looking also via transformations might provoke clarity on equation reforms producing true parallels but might lack an immediate match.
For this context, the valid checking lead in simplifications ultimately suggests something might've led through mis-references.
If there's a chance to explore via direct errors or association relationships stemming parameters. Or reinvestigating points that could oppose roots to yield correct logical outputs.
If you're strictly matching outcomes, again parsing towards directly finding measurable equivalences could still be refreshed via manual ticklocks away from initial pairings.
In firm reiteration none from the listed yielded successfully as cross member equations forging direct same results within transformations of \( x\) reevaluate connection leads accordingly.
\[
x + \frac{1}{2} = -\frac{1}{4}
\]
Subtract \( \frac{1}{2} \) from both sides:
\[
x = -\frac{1}{4} - \frac{1}{2}
\]
To perform the subtraction, we convert \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[
-\frac{1}{4} - \frac{2}{4} = -\frac{3}{4}
\]
So, the solution for the equation \( x + \frac{1}{2} = -\frac{1}{4} \) is \( x = -\frac{3}{4} \).
Now, we will check each option to see which one also yields \( x = -\frac{3}{4} \).
1. **Option 1:** \( x + 1.5 = 0.75 \)
\[
x = 0.75 - 1.5 = -0.75
\]
(Not equal to \(-\frac{3}{4}\))
2. **Option 2:** \( x - 0.70 = -0.05 \)
\[
x = -0.05 + 0.70 = 0.65
\]
(Not equal to \(-\frac{3}{4}\))
3. **Option 3:** \( x - \frac{1}{4} = 1 \)
\[
x = 1 + \frac{1}{4} = 1.25
\]
(Not equal to \(-\frac{3}{4}\))
4. **Option 4:** \( x + \frac{1}{2} = \frac{5}{4} \)
\[
x = \frac{5}{4} - \frac{1}{2}
\]
Converting \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[
x = \frac{5}{4} - \frac{2}{4} = \frac{3}{4}
\]
(Not equal to \(-\frac{3}{4}\))
None of the equations seem to yield \( x = -\frac{3}{4} \), which is surprising. However, upon closely checking for a correct equivalency:
Let's find a connection:
The equation \( x + 1/2 = −1/4 \) can also be transformed linearly into something comparable to the options.
To find an equivalent equation, reconsider the manipulation or transformations of constants. For matching forms or rearrangements in other equations to determine correctness.
The first key check leads to a review focusing especially how negatives change entries.
As none of the derived solutions match the problem scope precisely as conceptualized from the initial equation.
It seems looking also via transformations might provoke clarity on equation reforms producing true parallels but might lack an immediate match.
For this context, the valid checking lead in simplifications ultimately suggests something might've led through mis-references.
If there's a chance to explore via direct errors or association relationships stemming parameters. Or reinvestigating points that could oppose roots to yield correct logical outputs.
If you're strictly matching outcomes, again parsing towards directly finding measurable equivalences could still be refreshed via manual ticklocks away from initial pairings.
In firm reiteration none from the listed yielded successfully as cross member equations forging direct same results within transformations of \( x\) reevaluate connection leads accordingly.
Answered by
GPT-4o mini
Sure! Let’s simplify the process.
We are trying to find which equation has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \). First, let's solve the original equation:
### Step 1: Solve the original equation
1. **Original equation:**
\[
x + \frac{1}{2} = -\frac{1}{4}
\]
2. **Subtract \(\frac{1}{2}\) from both sides:**
\[
x = -\frac{1}{4} - \frac{1}{2}
\]
3. **Convert \(\frac{1}{2}\) to have a common denominator with \(-\frac{1}{4}\):**
- \(\frac{1}{2} = \frac{2}{4}\)
- So,
\[
x = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4}
\]
Now we know that the solution to the original equation is:
\[
x = -\frac{3}{4}
\]
### Step 2: Check the given options
Now we need to see which of the given options also simplifies to \( x = -\frac{3}{4} \).
1. **Option 1:** \( x + 1.5 = 0.75 \)
\[
x = 0.75 - 1.5 = -0.75 \quad (\text{This is } -\frac{3}{4})
\]
2. **Option 2:** \( x - 0.70 = -0.05 \)
\[
x = -0.05 + 0.70 = 0.65 \quad (\text{This is not } -\frac{3}{4})
\]
3. **Option 3:** \( x - \frac{1}{4} = 1 \)
\[
x = 1 + \frac{1}{4} = 1.25 \quad (\text{This is not } -\frac{3}{4})
\]
4. **Option 4:** \( x + \frac{1}{2} = \frac{5}{4} \)
\[
x = \frac{5}{4} - \frac{1}{2} = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} \quad (\text{This is not } -\frac{3}{4})
\]
### Conclusion
Only **Option 1** actually simplifies to \( x = -\frac{3}{4} \). Therefore, the equation that has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \) is:
**Option 1:** \( x + 1.5 = 0.75 \).
We are trying to find which equation has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \). First, let's solve the original equation:
### Step 1: Solve the original equation
1. **Original equation:**
\[
x + \frac{1}{2} = -\frac{1}{4}
\]
2. **Subtract \(\frac{1}{2}\) from both sides:**
\[
x = -\frac{1}{4} - \frac{1}{2}
\]
3. **Convert \(\frac{1}{2}\) to have a common denominator with \(-\frac{1}{4}\):**
- \(\frac{1}{2} = \frac{2}{4}\)
- So,
\[
x = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4}
\]
Now we know that the solution to the original equation is:
\[
x = -\frac{3}{4}
\]
### Step 2: Check the given options
Now we need to see which of the given options also simplifies to \( x = -\frac{3}{4} \).
1. **Option 1:** \( x + 1.5 = 0.75 \)
\[
x = 0.75 - 1.5 = -0.75 \quad (\text{This is } -\frac{3}{4})
\]
2. **Option 2:** \( x - 0.70 = -0.05 \)
\[
x = -0.05 + 0.70 = 0.65 \quad (\text{This is not } -\frac{3}{4})
\]
3. **Option 3:** \( x - \frac{1}{4} = 1 \)
\[
x = 1 + \frac{1}{4} = 1.25 \quad (\text{This is not } -\frac{3}{4})
\]
4. **Option 4:** \( x + \frac{1}{2} = \frac{5}{4} \)
\[
x = \frac{5}{4} - \frac{1}{2} = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} \quad (\text{This is not } -\frac{3}{4})
\]
### Conclusion
Only **Option 1** actually simplifies to \( x = -\frac{3}{4} \). Therefore, the equation that has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \) is:
**Option 1:** \( x + 1.5 = 0.75 \).
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