Question

Six times the sum of a number and 15 is −42.

Answer 1

Let's denote the unknown number as \( x \). According to the problem, six times the sum of this number and 15 can be expressed mathematically as follows:

\[
6(x + 15) = -42
\]

Now, we will solve this equation step-by-step.

1. First, divide both sides by 6 to simplify:

\[
x + 15 = \frac{-42}{6}
\]

Calculating the right side:

\[
\frac{-42}{6} = -7
\]

So the equation now is:

\[
x + 15 = -7
\]

2. Next, we subtract 15 from both sides to isolate \( x \):

\[
x = -7 - 15
\]

Calculating the right side:

\[
x = -22
\]

Thus, the solution to the equation is:

\[
\boxed{-22}
\]

To verify, we can substitute \( x = -22 \) back into the original statement:

1. Calculate the sum:

\[
-22 + 15 = -7
\]

2. Multiply by 6:

\[
6(-7) = -42
\]

Since the left-hand side matches the right-hand side of the original equation, our solution \( x = -22 \) is confirmed correct.