Question

Solve 9|x+5|−10=44 . Enter the larger value first.(1 point)
x= and x=

Answer 1

To solve the equation \( 9|x+5| - 10 = 44 \), we start by isolating the absolute value term.

1. Add 10 to both sides:
\[
9|x+5| = 54
\]

2. Divide both sides by 9:
\[
|x+5| = 6
\]

Now, we need to consider the two scenarios for the absolute value equation, \( |x+5| = 6 \).

**Case 1:**
\[
x + 5 = 6
\]
Subtracting 5 from both sides:
\[
x = 1
\]

**Case 2:**
\[
x + 5 = -6
\]
Subtracting 5 from both sides:
\[
x = -11
\]

Thus, the solutions to the equation are \( x = 1 \) and \( x = -11 \).

Now, we want to enter the larger value first:

\[
\text{Larger value: } x = 1, \quad \text{Smaller value: } x = -11
\]

So the final answer is:
\[
x = 1 \quad \text{and} \quad x = -11
\]