Question

|x| + 4 = 11
solve the equation for x. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. x =
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
b. there is no solution.
choose the correct graph below.
a.
number line with -15 to 15, dot at 6
b.
number line with -15 to 15, dots at -6 and 6
c.
number line with -15 to 15, dot at -6
d. there is no solution.

Explanation:

Step1: Solve the absolute value equation

To solve \(|x| + 4 = 11\), first subtract 4 from both sides:
\(|x| = 11 - 4\)
\(|x| = 7\)

Step2: Interpret the absolute value

The absolute value equation \(|x| = 7\) means \(x = 7\) or \(x = -7\) (since absolute value represents distance from 0 on the number line).

Step3: Identify the correct graph

• Graph A: Has a dot at \(x = 6\) (incorrect).
• Graph B: Has dots at \(x = -7\) and \(x = 7\)? Wait, no—wait, looking at the graphs:
• Graph B (middle bottom) has dots at \(x = -7\) (left) and \(x = 7\) (right)? Wait, no, the user’s graph labels:

Wait, recheck: The equation solutions are \(x = 7\) and \(x = -7\). So the graph with two dots: one at \(-7\) (left) and one at \(7\) (right) is Graph B? Wait, no, the options:
Wait, the graphs:

• Graph A: dot at \(x = 6\) (no).
• Graph B: dots at \(x = -7\) and \(x = 7\) (matches solutions \(x = 7, -7\)).
• Graph C: dot at \(x = -7\) (only one solution, incorrect).
• Graph D: no solution (incorrect).

Answer:

(for the equation): \(x = 7, -7\)