Let's solve the equation:
[tex]\[
\frac{9x}{8} - \frac{4}{3} = 2
\][/tex]
### Step-by-Step Solution:
1. Isolate the term with the variable [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we first need to move the constant term [tex]\(\frac{4}{3}\)[/tex] to the other side of the equation. We do this by adding [tex]\(\frac{4}{3}\)[/tex] to both sides of the equation:
[tex]\[
\frac{9x}{8} - \frac{4}{3} + \frac{4}{3} = 2 + \frac{4}{3}
\][/tex]
Simplifying this, we get:
[tex]\[
\frac{9x}{8} = 2 + \frac{4}{3}
\][/tex]
2. Create a common denominator for the right-hand side:
To add [tex]\(2\)[/tex] and [tex]\(\frac{4}{3}\)[/tex], we need a common denominator. The integer [tex]\(2\)[/tex] can be written as [tex]\(\frac{6}{3}\)[/tex] since [tex]\(2 = \frac{6}{3}\)[/tex]. Therefore:
[tex]\[
2 + \frac{4}{3} = \frac{6}{3} + \frac{4}{3}
\][/tex]
Adding these fractions:
[tex]\[
\frac{6}{3} + \frac{4}{3} = \frac{10}{3}
\][/tex]
So, our equation now is:
[tex]\[
\frac{9x}{8} = \frac{10}{3}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], we need to eliminate the fraction. We do this by multiplying both sides of the equation by the reciprocal of [tex]\(\frac{9}{8}\)[/tex], which is [tex]\(\frac{8}{9}\)[/tex]:
[tex]\[
\left(\frac{8}{9}\right) \cdot \frac{9x}{8} = \frac{10}{3} \cdot \left(\frac{8}{9}\right)
\][/tex]
On the left-hand side, the [tex]\(\frac{8}{9}\)[/tex] and the [tex]\(\frac{9}{8}\)[/tex] cancel out, leaving:
[tex]\[
x = \frac{10}{3} \cdot \frac{8}{9}
\][/tex]
4. Simplify the right-hand side:
Multiply the fractions on the right-hand side:
[tex]\[
x = \frac{10 \cdot 8}{3 \cdot 9} = \frac{80}{27}
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
x = \frac{80}{27} \approx 2.96296296296296
\][/tex]
