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

Let's break down the problem step by step.

Step 1: Write the Equation

The phrase "A number decreased by thirty-one is fifty-two" can be translated into a mathematical equation.

Let \( x \) represent the unknown number. The equation can be expressed as:

\[ x - 31 = 52 \]

Step 2: Solve the Equation

To solve for \( x \), you'll want to isolate \( x \) on one side. To do this, add 31 to both sides of the equation:

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

Step 3: Check the Solution

To verify that this solution is correct, substitute \( x \) back into the original equation:

\[ 83 - 31 = 52 \] Calculating the left side:

\[ 52 = 52 \]

The equation holds true, so the solution is correct.

Filling in the Blanks

Now, let's fill in the statements according to the process we just followed.

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

So the complete filled blanks will be:

• 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 use the check answer button now to confirm your statements are correct.