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.



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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.**