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,
substitute
99 for the variable in the equatio

Answer 1

Let's break down the statement into an equation. The phrase "A number decreased by twenty-four is thirteen" translates to:

**Equation:**
Let the unknown number be represented by \( x \).
The equation can be written as:
\[
x - 24 = 13
\]

This is a **subtraction** problem.

To solve the equation, **add** \( 24 \) to both sides of the equation:
\[
x - 24 + 24 = 13 + 24
\]
This simplifies to:
\[
x = 37
\]

To check the solution, substitute **37** for the variable in the equation:
- The original equation is \( x - 24 = 13 \).
- Substituting \( 37 \) gives us:
\[
37 - 24 = 13
\]
- Simplifying the left side results in:
\[
13 = 13
\]

Since both sides of the equation are equal, the solution is confirmed to be correct.

Therefore, the filled-out statements are:

- Equation: \( x - 24 = 13 \)
- This is a **subtraction** 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.