Certainly! Let's solve the given problem step-by-step.
The problem states:
"Twice the difference of a number and 8 is equal to three times the sum of the number and 3."
1. Define the variable:
Let [tex]\( x \)[/tex] be the number we need to find.
2. Set up the equation:
Twice the difference of a number and 8 can be written as:
[tex]\[
2(x - 8)
\][/tex]
Three times the sum of the number and 3 can be written as:
[tex]\[
3(x + 3)
\][/tex]
3. Form the equation:
According to the problem, these two expressions are equal. Therefore, we have:
[tex]\[
2(x - 8) = 3(x + 3)
\][/tex]
4. Simplify the equation:
Distribute the constants on both sides:
[tex]\[
2x - 16 = 3x + 9
\][/tex]
5. Isolate the variable:
Get all terms involving [tex]\( x \)[/tex] on one side of the equation and constants on the other side. We can start by subtracting [tex]\( 2x \)[/tex] from both sides:
[tex]\[
-16 = x + 9
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
Subtract 9 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
-25 = x
\][/tex]
So, the number is:
[tex]\[
x = -25
\][/tex]
Thus, the solution to the problem is [tex]\( -25 \)[/tex].
