Express the following as algebraic equations and solve.
Five times a number increased by 2 is 12. What is the number?

Answer

To express the given statement as an algebraic equation and solve for the unknown number, follow these steps:

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Translate the verbal statement into an equation
The statement "Five times a number increased by 2 is 12" can be translated into the following equation:
\[ 5x + 2 = 12 \]

### Step 3: Isolate the variable term
To isolate the term with \( x \), subtract 2 from both sides of the equation:
\[ 5x + 2 - 2 = 12 - 2 \]
This simplifies to:
\[ 5x = 10 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 5 to solve for \( x \):
\[ x = \frac{10}{5} \]
This simplifies to:
\[ x = 2 \]

### Conclusion
The number is \( 2 \).

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