Of course, let's solve each of these equations step-by-step.
### Equation (xi): [tex]\(\frac{x}{4} = \frac{9}{8}\)[/tex]
1. Our goal is to solve for [tex]\( x \)[/tex]. Start with the given equation:
[tex]\[
\frac{x}{4} = \frac{9}{8}
\][/tex]
2. To isolate [tex]\( x \)[/tex], multiply both sides of the equation by 4:
[tex]\[
x = \left(\frac{9}{8}\right) \times 4
\][/tex]
3. Simplify [tex]\(\left(\frac{9}{8}\right) \times 4\)[/tex]:
[tex]\[
x = \frac{9 \times 4}{8} = \frac{36}{8} = 4.5
\][/tex]
So, the solution to the first equation is:
[tex]\[
x = 4.5
\][/tex]
### Equation (xiv): [tex]\(\frac{1}{2} - 3x = 0\)[/tex]
1. Our goal is to solve for [tex]\( x \)[/tex]. Start with the given equation:
[tex]\[
\frac{1}{2} - 3x = 0
\][/tex]
2. Subtract [tex]\(\frac{1}{2}\)[/tex] from both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[
-3x = -\frac{1}{2}
\][/tex]
3. Divide both sides by -3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-\frac{1}{2}}{-3} = \frac{1}{6}
\][/tex]
So, the solution to the second equation is:
[tex]\[
x = \frac{1}{6}
\][/tex]
Thus, the solutions to the given equations are:
1. For [tex]\(\frac{x}{4} = \frac{9}{8}\)[/tex], [tex]\( x = 4.5 \)[/tex]
2. For [tex]\(\frac{1}{2} - 3x = 0\)[/tex], [tex]\( x = \frac{1}{6} \)[/tex]
