Sure, let's solve the equation [tex]\(\frac{x}{2} + \frac{1}{3} \frac{(x)}{2} = 120\)[/tex] step by step.
1. Combine the fractions on the left side of the equation:
Given equation:
[tex]\[
\frac{x}{2} + \frac{1}{3} \frac{(x)}{2} = 120
\][/tex]
To simplify, we can rewrite [tex]\(\frac{1}{3} \frac{(x)}{2}\)[/tex] as [tex]\(\frac{x}{6}\)[/tex]:
[tex]\[
\frac{x}{2} + \frac{x}{6} = 120
\][/tex]
2. Find a common denominator:
The least common denominator for [tex]\(\frac{x}{2}\)[/tex] and [tex]\(\frac{x}{6}\)[/tex] is 6. To combine the fractions, we convert them to have the same denominator:
[tex]\[
\frac{x}{2} = \frac{3x}{6}
\][/tex]
So, we rewrite the equation as:
[tex]\[
\frac{3x}{6} + \frac{x}{6} = 120
\][/tex]
3. Combine the fractions:
Now, combine the fractions on the left side:
[tex]\[
\frac{3x + x}{6} = \frac{4x}{6}
\][/tex]
Simplify the fraction:
[tex]\[
\frac{2x}{3} = 120
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], multiply both sides of the equation by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
x = 120 \times \frac{3}{2}
\][/tex]
Calculate the right side:
[tex]\[
x = 180
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{180}\)[/tex].
