Question
Which value of x satisfies the equation one half, left parenthesis, x, minus, one half, right parenthesis, equals, start fraction, 15, divided by, 4, end fraction
2
1
(x−
2
1
)=
4
15
?
2
1
(x−
2
1
)=
4
15
?
Answers
GPT-4o mini
To solve the equation
\[
\frac{1}{2} \left( x - \frac{1}{2} \right) = \frac{15}{4},
\]
we first eliminate the fraction by multiplying both sides of the equation by 2:
\[
x - \frac{1}{2} = \frac{15}{4} \cdot 2
\]
Calculating the right side:
\[
x - \frac{1}{2} = \frac{15 \cdot 2}{4} = \frac{30}{4} = \frac{15}{2}
\]
Next, we add \(\frac{1}{2}\) to both sides of the equation:
\[
x = \frac{15}{2} + \frac{1}{2}
\]
Since \(\frac{15}{2} + \frac{1}{2} = \frac{15 + 1}{2} = \frac{16}{2} = 8\), we find:
\[
x = 8
\]
Thus, the value of \(x\) that satisfies the equation is:
\[
\boxed{8}
\]
\[
\frac{1}{2} \left( x - \frac{1}{2} \right) = \frac{15}{4},
\]
we first eliminate the fraction by multiplying both sides of the equation by 2:
\[
x - \frac{1}{2} = \frac{15}{4} \cdot 2
\]
Calculating the right side:
\[
x - \frac{1}{2} = \frac{15 \cdot 2}{4} = \frac{30}{4} = \frac{15}{2}
\]
Next, we add \(\frac{1}{2}\) to both sides of the equation:
\[
x = \frac{15}{2} + \frac{1}{2}
\]
Since \(\frac{15}{2} + \frac{1}{2} = \frac{15 + 1}{2} = \frac{16}{2} = 8\), we find:
\[
x = 8
\]
Thus, the value of \(x\) that satisfies the equation is:
\[
\boxed{8}
\]