Sure! Let's solve the equation step-by-step.
The given equation is:
[tex]\[
\frac{2}{3} x - 5 = 21
\][/tex]
Step 1: Isolate the term involving [tex]\( x \)[/tex].
To do this, we add 5 to both sides of the equation:
[tex]\[
\frac{2}{3} x - 5 + 5 = 21 + 5
\][/tex]
This simplifies to:
[tex]\[
\frac{2}{3} x = 26
\][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
To isolate [tex]\( x \)[/tex], we need to get rid of the fraction [tex]\(\frac{2}{3}\)[/tex]. We can do this by multiplying both sides of the equation by the reciprocal of [tex]\(\frac{2}{3}\)[/tex], which is [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
\left(\frac{3}{2}\right) \cdot \frac{2}{3} x = 26 \cdot \left(\frac{3}{2}\right)
\][/tex]
The left side simplifies to [tex]\( x \)[/tex]:
[tex]\[
x = 26 \cdot \left(\frac{3}{2}\right)
\][/tex]
Then, we calculate:
[tex]\[
x = \frac{26 \cdot 3}{2}
\][/tex]
[tex]\[
x = \frac{78}{2}
\][/tex]
[tex]\[
x = 39
\][/tex]
So, the solution to the equation [tex]\(\frac{2}{3} x - 5 = 21\)[/tex] is:
[tex]\[
x = 39
\][/tex]
Among the options [tex]\(x = 24\)[/tex], [tex]\(x = 39\)[/tex], [tex]\(x = \frac{42}{3}\)[/tex], and [tex]\(x = \frac{32}{3}\)[/tex], the correct one is:
[tex]\[
x = 39
\][/tex]
