Question

Write an equation to model each situation. Then solve the equation
1. Three times a number plus 12 minus 5 times the same number is 22. What is the number?

Answer 1

To model the situation, let's define the unknown number as \( x \). The equation based on the description provided is:

\[
3x + 12 - 5x = 22
\]

Now, we will simplify and solve the equation:

1. Combine like terms on the left side:

\[
(3x - 5x) + 12 = 22
\]

This simplifies to:

\[
-2x + 12 = 22
\]

2. Next, subtract 12 from both sides:

\[
-2x + 12 - 12 = 22 - 12
\]

This simplifies to:

\[
-2x = 10
\]

3. Now, we divide both sides by -2 to solve for \( x \):

\[
x = \frac{10}{-2}
\]

This simplifies to:

\[
x = -5
\]

Therefore, the number is \( \boxed{-5} \).