To solve the equation [tex]\(\frac{x}{4} = \frac{9}{2}\)[/tex], follow these steps:
1. Understand the equation:
The equation [tex]\(\frac{x}{4} = \frac{9}{2}\)[/tex] means that some value [tex]\(x\)[/tex] divided by 4 is equal to 9 divided by 2.
2. Eliminate the fraction:
To clear the fraction and solve for [tex]\(x\)[/tex], you can multiply both sides of the equation by 4 (the denominator on the left side):
[tex]\[
4 \cdot \left(\frac{x}{4}\right) = 4 \cdot \left(\frac{9}{2}\right)
\][/tex]
3. Simplify the equation:
On the left side, [tex]\(4 \cdot \left(\frac{x}{4}\right)\)[/tex] simplifies to [tex]\(x\)[/tex], because the 4s cancel out. On the right side, you multiply:
[tex]\[
x = 4 \cdot \frac{9}{2}
\][/tex]
4. Perform the multiplication:
[tex]\[
x = 4 \cdot \frac{9}{2}
\][/tex]
This can be simplified by multiplying 4 with 9 first, and then dividing by 2:
[tex]\[
x = \frac{4 \cdot 9}{2}
\][/tex]
[tex]\[
x = \frac{36}{2}
\][/tex]
5. Divide to find [tex]\(x\)[/tex]:
[tex]\[
x = 18
\][/tex]
6. Check your solution:
Substitute [tex]\(x = 18\)[/tex] back into the original equation to ensure it is correct:
[tex]\[
\frac{18}{4} = \frac{9}{2}
\][/tex]
Simplifying the left side:
[tex]\[
\frac{18}{4} = \frac{9}{2}
\][/tex]
Both sides are indeed equal, confirming our solution is correct.
Therefore, the solution to the equation [tex]\(\frac{x}{4} = \frac{9}{2}\)[/tex] is [tex]\(x = 18\)[/tex].
