Let's solve the equation [tex]\(\frac{54}{h-1} = 3\)[/tex] step-by-step.
1. Remove the denominator:
To eliminate the fraction, multiply both sides of the equation by [tex]\((h - 1)\)[/tex]:
[tex]\[
54 = 3 \cdot (h - 1)
\][/tex]
2. Distribute the 3 on the right side:
Now distribute the [tex]\(3\)[/tex] inside the parenthesis:
[tex]\[
54 = 3h - 3
\][/tex]
3. Isolate the term with [tex]\(h\)[/tex]:
Add [tex]\(3\)[/tex] to both sides of the equation to move the constant term:
[tex]\[
54 + 3 = 3h
\][/tex]
Simplify it:
[tex]\[
57 = 3h
\][/tex]
4. Solve for [tex]\(h\)[/tex]:
To isolate [tex]\(h\)[/tex], divide both sides of the equation by [tex]\(3\)[/tex]:
[tex]\[
h = \frac{57}{3}
\][/tex]
Simplify it:
[tex]\[
h = 19
\][/tex]
Thus, the value of [tex]\(h\)[/tex] is [tex]\(19\)[/tex].
