Sure, let's solve the problem step-by-step.
First, we need to represent the verbal sentence as a mathematical equation. The sentence states: "When [tex]\(\frac{5}{2}\)[/tex] of a number is subtracted from 18, the result is 3."
1. Let [tex]\( x \)[/tex] represent the unknown number.
2. According to the problem, [tex]\(\frac{5}{2}\)[/tex] of the number [tex]\( x \)[/tex] is subtracted from 18. This can be written as:
[tex]\[
18 - \frac{5}{2}x = 3
\][/tex]
Next, we need to solve this equation for [tex]\( x \)[/tex]. Here are the steps:
3. Start by isolating the term involving [tex]\( x \)[/tex]. To do this, subtract 18 from both sides of the equation:
[tex]\[
18 - \frac{5}{2}x - 18 = 3 - 18
\][/tex]
Simplifying this, we get:
[tex]\[
-\frac{5}{2}x = -15
\][/tex]
4. To solve for [tex]\( x \)[/tex], we need to get rid of the coefficient [tex]\(-\frac{5}{2}\)[/tex]. Multiply both sides of the equation by the reciprocal of [tex]\(-\frac{5}{2}\)[/tex], which is [tex]\(-\frac{2}{5}\)[/tex]:
[tex]\[
x = (-15) \times \left(-\frac{2}{5}\right)
\][/tex]
5. Now, perform the multiplication:
[tex]\[
x = \frac{30}{5}
\][/tex]
Simplifying the fraction, we find:
[tex]\[
x = 6
\][/tex]
So, the number is [tex]\( 6 \)[/tex].
