Asked by nope
Solve for x.
58(x+1/2)=100
(1 point)
Responses
160 1/2
160 and 1 half
62
62
159 1/2
159 and 1 half
63
58(x+1/2)=100
(1 point)
Responses
160 1/2
160 and 1 half
62
62
159 1/2
159 and 1 half
63
Answers
Answered by
nope
5/8(x+1/2)=100
Answered by
GPT-4o mini
To solve the equation \(58(x + \frac{1}{2}) = 100\), we can follow these steps:
1. **Distribute the 58** across the parentheses:
\[
58x + 29 = 100
\]
2. **Subtract 29 from both sides**:
\[
58x = 100 - 29
\]
\[
58x = 71
\]
3. **Divide both sides by 58**:
\[
x = \frac{71}{58}
\]
4. **Simplify the fraction**:
- \(71\) and \(58\) have no common factors, so we keep it as \(\frac{71}{58}\).
- Converting \(\frac{71}{58}\) to a mixed number:
\[
71 \div 58 = 1 \text{ R } 13
\]
Therefore,
\[
x = 1 \frac{13}{58}
\]
Since none of the responses from the provided options seem to directly match \(\frac{71}{58}\) or its decimal equivalent, a check of the possible answers given (160 1/2, 62, 159 1/2, 63) reveals that they do not correspond to our calculated value of \(x\).
Thus, let's compute \( \frac{71}{58} \) as a decimal for clarity:
\[
\frac{71}{58} \approx 1.224137931
\]
If you belong to a specific answer format aiming for mixed numbers, fractional forms, or the like, please provide clarification for proper interpretation—but per my calculation, normalizing from above gives \(x \approx 1.22\) or as approximated \(1 \frac{13}{58}\).
To summarize, please refer to the original solutions prompted earlier in hypothetical ranges; thus the direct interpretation from the input values did not yield \(x\) in predictable ranges confirmed. However, none of the choices outlined correspond accordingly to the result achieved through the algebraic resolution.
1. **Distribute the 58** across the parentheses:
\[
58x + 29 = 100
\]
2. **Subtract 29 from both sides**:
\[
58x = 100 - 29
\]
\[
58x = 71
\]
3. **Divide both sides by 58**:
\[
x = \frac{71}{58}
\]
4. **Simplify the fraction**:
- \(71\) and \(58\) have no common factors, so we keep it as \(\frac{71}{58}\).
- Converting \(\frac{71}{58}\) to a mixed number:
\[
71 \div 58 = 1 \text{ R } 13
\]
Therefore,
\[
x = 1 \frac{13}{58}
\]
Since none of the responses from the provided options seem to directly match \(\frac{71}{58}\) or its decimal equivalent, a check of the possible answers given (160 1/2, 62, 159 1/2, 63) reveals that they do not correspond to our calculated value of \(x\).
Thus, let's compute \( \frac{71}{58} \) as a decimal for clarity:
\[
\frac{71}{58} \approx 1.224137931
\]
If you belong to a specific answer format aiming for mixed numbers, fractional forms, or the like, please provide clarification for proper interpretation—but per my calculation, normalizing from above gives \(x \approx 1.22\) or as approximated \(1 \frac{13}{58}\).
To summarize, please refer to the original solutions prompted earlier in hypothetical ranges; thus the direct interpretation from the input values did not yield \(x\) in predictable ranges confirmed. However, none of the choices outlined correspond accordingly to the result achieved through the algebraic resolution.
Answered by
GPT-4o mini
To solve the equation
\[
\frac{5}{8}(x + \frac{1}{2}) = 100,
\]
follow these steps:
1. **Multiply both sides by the reciprocal of \(\frac{5}{8}\)** to eliminate the fraction. The reciprocal is \(\frac{8}{5}\):
\[
x + \frac{1}{2} = 100 \cdot \frac{8}{5}
\]
2. **Calculate the right-hand side**:
\[
100 \cdot \frac{8}{5} = 100 \cdot 1.6 = 160
\]
So we have:
\[
x + \frac{1}{2} = 160
\]
3. **Subtract \(\frac{1}{2}\) from both sides** to isolate \(x\):
\[
x = 160 - \frac{1}{2}
\]
Converting 160 into halves:
\[
x = \frac{320}{2} - \frac{1}{2} = \frac{319}{2}
\]
4. **Convert \(\frac{319}{2}\) into a mixed number**:
\[
\frac{319}{2} = 159 \frac{1}{2}
\]
Thus, the solution to the equation is
\[
x = 159 \frac{1}{2} \text{ or } 159.5.
\]
In terms of the answer choices you provided earlier, the correct response is
**159 1/2**.
\[
\frac{5}{8}(x + \frac{1}{2}) = 100,
\]
follow these steps:
1. **Multiply both sides by the reciprocal of \(\frac{5}{8}\)** to eliminate the fraction. The reciprocal is \(\frac{8}{5}\):
\[
x + \frac{1}{2} = 100 \cdot \frac{8}{5}
\]
2. **Calculate the right-hand side**:
\[
100 \cdot \frac{8}{5} = 100 \cdot 1.6 = 160
\]
So we have:
\[
x + \frac{1}{2} = 160
\]
3. **Subtract \(\frac{1}{2}\) from both sides** to isolate \(x\):
\[
x = 160 - \frac{1}{2}
\]
Converting 160 into halves:
\[
x = \frac{320}{2} - \frac{1}{2} = \frac{319}{2}
\]
4. **Convert \(\frac{319}{2}\) into a mixed number**:
\[
\frac{319}{2} = 159 \frac{1}{2}
\]
Thus, the solution to the equation is
\[
x = 159 \frac{1}{2} \text{ or } 159.5.
\]
In terms of the answer choices you provided earlier, the correct response is
**159 1/2**.
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