Question

Write and solve the equation and then check your answer. Select the correct statements for each blank.

A number decreased by twenty-four is thirteen.



(5 points)
Equation: ________

This is a ________ problem.

To solve the equation, ______ ____ to both sides of the equation.

To check the solution, ___________99 for the variable in the equation.

Answer 1

Let's solve the problem step-by-step.

1. **Translate the statement into an equation:**
"A number decreased by twenty-four is thirteen."
Let the unknown number be represented by \( x \). The equation can be written as:
\[
x - 24 = 13
\]

So, the equation is:
\[
\text{Equation: } x - 24 = 13
\]

2. **Identify the type of problem:**
This is a basic algebraic equation problem.
\[
\text{This is a } \text{basic algebraic} \text{ problem.}
\]

3. **Determine the steps to solve the equation:**
To isolate \( x \), we need to add \( 24 \) to both sides of the equation.
\[
\text{To solve the equation, } \text{add } 24 \text{ to both sides of the equation.}
\]

Now, solving:
\[
x - 24 + 24 = 13 + 24
\]
\[
x = 37
\]

4. **Check the solution:**
To verify, we substitute \( 37 \) back into the original equation:
\[
37 - 24 = 13
\]
The left side becomes:
\[
13 = 13
\]
This is true, confirming that our solution is correct.

Thus,
\[
\text{To check the solution, substitute } 37 \text{ for the variable in the equation.}
\]

Now putting everything together:

- **Equation:** \( x - 24 = 13 \)
- **This is a:** basic algebraic problem.
- **To solve the equation,:** add 24 to both sides of the equation.
- **To check the solution,:** substitute 37 for the variable in the equation.