Sure! Let's tackle the problem step-by-step.
1. Define the variable: Let's denote the unknown number by [tex]\( x \)[/tex].
2. Set up the equation:
According to the problem, "7 more than twice a number" can be written as:
[tex]\[
2x + 7
\][/tex]
Similarly, "3 less than three times the same number" can be expressed as:
[tex]\[
3x - 3
\][/tex]
These two expressions are said to be equal, so we set up the equation:
[tex]\[
2x + 7 = 3x - 3
\][/tex]
3. Solve the equation:
First, we want to isolate [tex]\( x \)[/tex]. To do this, we'll start by eliminating [tex]\( x \)[/tex] from one side of the equation:
[tex]\[
2x + 7 = 3x - 3
\][/tex]
Subtract [tex]\( 2x \)[/tex] from both sides to get:
[tex]\[
7 = x - 3
\][/tex]
Next, we'll isolate [tex]\( x \)[/tex] by adding 3 to both sides:
[tex]\[
7 + 3 = x
\][/tex]
[tex]\[
x = 10
\][/tex]
4. Conclusion:
The number that satisfies the condition "7 more than twice a number is 3 less than three times the same number" is:
[tex]\[
\boxed{10}
\][/tex]
