Question

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

A number decreased by sixty-eight is thirty-one.



(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 break down the problem step-by-step.

1. **Write the equation:**
Let the unknown number be represented by \( x \). According to the statement "A number decreased by sixty-eight is thirty-one," we can write the equation as:
\[
x - 68 = 31
\]

2. **Identify the problem type:**
This is a **linear equation** problem.

3. **Solve the equation:**
To solve for \( x \), we add 68 to both sides of the equation:
\[
x - 68 + 68 = 31 + 68
\]
Simplifying both sides gives:
\[
x = 99
\]

4. **Check the solution:**
To check the solution, substitute \( 99 \) for \( x \) in the original equation:
\[
99 - 68 = 31
\]
Performing the calculation:
\[
31 = 31
\]
This is true, so the solution is verified.

Now, filling in the statements:

- Equation: \( x - 68 = 31 \)
- This is a **linear** problem.
- To solve the equation, **add 68** to both sides of the equation.
- To check the solution, **substitute 99** for the variable in the equation.