Sure, let's solve each equation step by step.
### Part (a)
Solve the equation [tex]\(\frac{2x}{3} = 8\)[/tex]:
1. Isolate the variable [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], first multiply both sides of the equation by 3 to get rid of the denominator:
[tex]\[
3 \cdot \frac{2x}{3} = 3 \cdot 8
\][/tex]
This simplifies to:
[tex]\[
2x = 24
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now, divide both sides by 2:
[tex]\[
x = \frac{24}{2}
\][/tex]
This simplifies to:
[tex]\[
x = 12
\][/tex]
So, the solution to part (a) is [tex]\(x = 12\)[/tex].
### Part (b)
Solve the equation [tex]\(\frac{3x}{2} = 6\)[/tex]:
1. Isolate the variable [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], first multiply both sides of the equation by 2 to get rid of the denominator:
[tex]\[
2 \cdot \frac{3x}{2} = 2 \cdot 6
\][/tex]
This simplifies to:
[tex]\[
3x = 12
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now, divide both sides by 3:
[tex]\[
x = \frac{12}{3}
\][/tex]
This simplifies to:
[tex]\[
x = 4
\][/tex]
So, the solution to part (b) is [tex]\(x = 4\)[/tex].
### Summary
For the given equations:
- The solution to [tex]\(\frac{2x}{3} = 8\)[/tex] is [tex]\(x = 12\)[/tex].
- The solution to [tex]\(\frac{3x}{2} = 6\)[/tex] is [tex]\(x = 4\)[/tex].
