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

Question

A number decreased by thirty-one is fifty-two.



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(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 work through the problem step by step, let's start by translating the word problem into an equation.

1. Write the equation: Let \( x \) be the unknown number. The phrase "A number decreased by thirty-one" translates to \( x - 31 \). The statement "is fifty-two" translates to \( = 52 \). Thus, the equation becomes: \[ x - 31 = 52 \]

2. Identify the type of problem: This is a linear problem.

3. To solve the equation: To isolate \( x \), we need to add 31 to both sides of the equation. The steps would look like this: \[ x - 31 + 31 = 52 + 31 \] Simplifying this gives: \[ x = 83 \]

4. To check the solution: Substitute \( 83 \) for the variable \( x \) in the original equation: \[ 83 - 31 = 52 \] Simplifying the left side: \[ 52 = 52 \] Since both sides are equal, the solution is confirmed as correct.

Now, let's fill in the blanks with the correct statements.

Equation: \( x - 31 = 52 \)

This is a linear problem.

To solve the equation, add 31 to both sides of the equation.

To check the solution, substitute 83 for the variable in the equation.