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