Question
Which value of x satisfies the equation start fraction, 5, divided by, 4, end fraction, left parenthesis, x, plus, one sixth, right parenthesis, equals, minus, start fraction, 205, divided by, 24, end fraction
4
5
(x+
6
1
)=−
24
205
?
Answer
Multiple Choice Answers
66
minus, 6−6
77
minus, 7−7
4
5
(x+
6
1
)=−
24
205
?
Answer
Multiple Choice Answers
66
minus, 6−6
77
minus, 7−7
Answers
GPT-4o mini
To solve the equation
\[
\frac{5}{4} \left( x + \frac{1}{6} \right) = -\frac{205}{24},
\]
first, we can eliminate the fraction on the left side by multiplying both sides by 4:
\[
5 \left( x + \frac{1}{6} \right) = -\frac{205 \times 4}{24}.
\]
Now simplify the right side:
\[
-\frac{205 \times 4}{24} = -\frac{820}{24} = -\frac{205}{6}.
\]
Next, we have:
\[
5 \left( x + \frac{1}{6} \right) = -\frac{205}{6}.
\]
Now, divide both sides by 5:
\[
x + \frac{1}{6} = -\frac{205}{6 \times 5} = -\frac{205}{30} = -\frac{41}{6}.
\]
Now, isolate \(x\) by subtracting \(\frac{1}{6}\) from both sides:
\[
x = -\frac{41}{6} - \frac{1}{6} = -\frac{41 + 1}{6} = -\frac{42}{6} = -7.
\]
Thus, the value of \(x\) that satisfies the equation is:
\[
\boxed{-7}.
\]
\[
\frac{5}{4} \left( x + \frac{1}{6} \right) = -\frac{205}{24},
\]
first, we can eliminate the fraction on the left side by multiplying both sides by 4:
\[
5 \left( x + \frac{1}{6} \right) = -\frac{205 \times 4}{24}.
\]
Now simplify the right side:
\[
-\frac{205 \times 4}{24} = -\frac{820}{24} = -\frac{205}{6}.
\]
Next, we have:
\[
5 \left( x + \frac{1}{6} \right) = -\frac{205}{6}.
\]
Now, divide both sides by 5:
\[
x + \frac{1}{6} = -\frac{205}{6 \times 5} = -\frac{205}{30} = -\frac{41}{6}.
\]
Now, isolate \(x\) by subtracting \(\frac{1}{6}\) from both sides:
\[
x = -\frac{41}{6} - \frac{1}{6} = -\frac{41 + 1}{6} = -\frac{42}{6} = -7.
\]
Thus, the value of \(x\) that satisfies the equation is:
\[
\boxed{-7}.
\]