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**:
The statement "A number decreased by sixty-eight is thirty-one" can be translated into the equation:
\[
x - 68 = 31
\]
where \( x \) is the number we're trying to find.

2. **Solve the equation**:
To solve for \( x \), we need to isolate \( x \) on one side. We do this by adding 68 to both sides of the equation:
\[
x - 68 + 68 = 31 + 68
\]
Simplifying this gives:
\[
x = 99
\]

3. **Check the solution**:
Now we check the solution by substituting \( 99 \) back into the original equation:
\[
99 - 68 = 31
\]
Simplifying the left side:
\[
31 = 31
\]
This statement is true, so our solution is verified.

Now, we can fill in the blanks based on the above steps:

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

These statements accurately convey the steps taken to solve the problem.