Question

Write and solve the equation and then check your answer. Select the correct statements for each blank.A number decreased by thirty-one is fifty-two. NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.(5 points)Equation: This is a problem.To solve the equation, to both sides of the equation.To check the solution, 83 for the variable in the equation.

Answer 1

To write and solve the equation based on the statement "A number decreased by thirty-one is fifty-two," we can define the unknown number as \( x \).

### Step 1: Write the Equation
The equation based on the problem is:
\[ x - 31 = 52 \]

### Step 2: Solve the Equation
To solve for \( x \), we need to isolate \( x \) on one side of the equation. We do this by adding 31 to both sides:

\[ x - 31 + 31 = 52 + 31 \]
\[ x = 83 \]

### Step 3: Check the Solution
To verify our solution, we will substitute \( x = 83 \) back into the original equation:

- The original equation is \( x - 31 = 52 \).
- Substitute \( 83 \) in for \( x \):

\[ 83 - 31 = 52 \]
\[ 52 = 52 \]

This confirms that our solution is correct.

### Summary
- **Equation:** \( x - 31 = 52 \)
- **To solve the equation,** add 31 to both sides of the equation.
- **To check the solution,** substitute \( 83 \) for the variable in the equation.

You can click the "check answer" button now to see if this is correct!