Certainly! Let's solve the problem step by step.
### Step 1: Define the unknown
Let the unknown number be [tex]\( x \)[/tex].
### Step 2: Set up the equation based on the problem statement
- The problem states that 5 is added to a number, which we wrote as [tex]\( x + 5 \)[/tex].
- This result is 7 less than three times the number, written as [tex]\( 3x - 7 \)[/tex].
### Step 3: Formulate the equation
We can set up the equation as:
[tex]\[ x + 5 = 3x - 7 \][/tex]
### Step 4: Solve for [tex]\( x \)[/tex]
To isolate [tex]\( x \)[/tex], we'll perform algebraic operations:
1. Subtract [tex]\( x \)[/tex] from both sides to get the terms involving [tex]\( x \)[/tex] on one side:
[tex]\[ 5 = 2x - 7 \][/tex]
2. Add 7 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 12 = 2x \][/tex]
3. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 6 \][/tex]
### Conclusion
Therefore, the number is [tex]\( 6 \)[/tex].
