Certainly! Let's solve the problem step-by-step.
We are given that when a number is multiplied by 6, the result is increased by 45. We need to find that number. Let's denote the unknown number by [tex]\( x \)[/tex].
1. Set up the equation: According to the problem, multiplying the number by 6 gives the same result as adding 45 to the number.
[tex]\[
6x = x + 45
\][/tex]
2. Isolate the variable [tex]\( x \)[/tex]: To solve for [tex]\( x \)[/tex], we first need to get all the [tex]\( x \)[/tex] terms on one side of the equation. Let's subtract [tex]\( x \)[/tex] from both sides.
[tex]\[
6x - x = x + 45 - x
\][/tex]
Simplifying this, we get:
[tex]\[
5x = 45
\][/tex]
3. Solve for [tex]\( x \)[/tex]: Now, divide both sides of the equation by 5 to isolate [tex]\( x \)[/tex].
[tex]\[
x = \frac{45}{5}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 9
\][/tex]
So, the number is [tex]\( 9 \)[/tex].
To verify, we can substitute [tex]\( 9 \)[/tex] back into the original statement:
- Multiplying [tex]\( 9 \)[/tex] by 6 gives [tex]\( 54 \)[/tex].
- Adding 45 to [tex]\( 9 \)[/tex] gives [tex]\( 54 \)[/tex].
Both operations result in [tex]\( 54 \)[/tex], confirming that our solution is correct. Thus, the number is indeed [tex]\( 9 \)[/tex].
