Reed Hilton
01/02/2024 · Elementary School
\( = 3 _ { 3 } ^ { 1 } ( 3 - 2 x ) = 10 ( x - \frac { 1 } { 2 } ) \)
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Step-by-step Solution
To solve the equation
\[
3_{3}^{1} (3 - 2x) = 10 \left( x - \frac{1}{2} \right),
\]
we first need to clarify the notation. The notation \(3_{3}^{1}\) is not standard in mathematics. If we assume it means simply \(3\), we can rewrite the equation as:
\[
3(3 - 2x) = 10 \left( x - \frac{1}{2} \right).
\]
Now, let's simplify both sides of the equation.
Starting with the left side:
\[
3(3 - 2x) = 9 - 6x.
\]
Now, simplifying the right side:
\[
10 \left( x - \frac{1}{2} \right) = 10x - 5.
\]
Now we have the equation:
\[
9 - 6x = 10x - 5.
\]
Next, we will move all terms involving \(x\) to one side and constant terms to the other side. Adding \(6x\) to both sides gives:
\[
9 = 16x - 5.
\]
Now, add \(5\) to both sides:
\[
14 = 16x.
\]
Now, divide both sides by \(16\):
\[
x = \frac{14}{16} = \frac{7}{8}.
\]
Thus, the solution to the equation is:
\[
\boxed{\frac{7}{8}}.
\]
Quick Answer
The solution to the equation is \( x = \frac{7}{8} \).
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