Sure, let's solve the equation step by step.
### Step 1: Addition Property of Equality
We start with the given equation:
[tex]\[
\frac{1}{5}x - \frac{2}{3} = \frac{4}{3}
\][/tex]
To isolate the term with [tex]\( x \)[/tex], we need to get rid of [tex]\( -\frac{2}{3} \)[/tex] on the left side. We do this by adding [tex]\( \frac{2}{3} \)[/tex] to both sides of the equation:
[tex]\[
\frac{1}{5}x - \frac{2}{3} + \frac{2}{3} = \frac{4}{3} + \frac{2}{3}
\][/tex]
Simplifying both sides:
[tex]\[
\frac{1}{5}x = \frac{6}{3}
\][/tex]
### Step 2: Multiplicative Property of Equality
Next, we need to isolate [tex]\( x \)[/tex] by removing the fraction [tex]\( \frac{1}{5} \)[/tex]. We do this by multiplying both sides of the equation by 5:
[tex]\[
\frac{1}{5}x \cdot 5 = 2 \cdot 5
\][/tex]
Simplifying both sides:
[tex]\[
x = 10
\][/tex]
Therefore, the solution is:
[tex]\[
x = 10
\][/tex]
