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.

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 start by translating the verbal statement into an equation.

The statement "A number decreased by sixty-eight is thirty-one" can be expressed as:

**Equation:** \( x - 68 = 31 \)

This is a **subtraction** problem.

To solve the equation, **add 68** to both sides of the equation.

Now, let's solve it:

1. Start with the equation:
\[
x - 68 = 31
\]
2. Add 68 to both sides:
\[
x - 68 + 68 = 31 + 68
\]
\[
x = 99
\]

To check the solution, **substitute 99 for the variable in the equation**:

1. Replace \( x \) with 99 in the original equation:
\[
99 - 68 = 31
\]
2. Simplifying the left side:
\[
31 = 31
\]

Since both sides are equal, the solution is verified.

Now filling in the blanks:

- **Equation:** \( x - 68 = 31 \)
- This is a **subtraction** 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.