Questions: Solve the equation. Then graph the solution set. f+10=1

Solution Steps

To solve the equation \(|f+10|=1\), we need to consider the definition of absolute value. The equation \(|f+10|=1\) implies two possible cases: \(f+10=1\) and \(f+10=-1\). We will solve these two linear equations separately to find the values of \(f\). After finding the solutions, we can graph them on a number line.

The given equation is:

\[ |f + 10| = 1 \]

An absolute value equation of the form \(|x| = a\) implies two possible equations:

1. \(x = a\)
2. \(x = -a\)

For the equation \(|f + 10| = 1\), we set up the two possible equations:

1. \(f + 10 = 1\)
2. \(f + 10 = -1\)

Subtract 10 from both sides:

\[ f = 1 - 10 \]

\[ f = -9 \]

Subtract 10 from both sides:

\[ f = -1 - 10 \]

\[ f = -11 \]

The solution set consists of the values \(f = -9\) and \(f = -11\). On a number line, these are two distinct points:

• Plot a point at \(f = -9\).
• Plot a point at \(f = -11\).

Final Answer