Solve the equation. Graph and check your solutions.

Question

lxl+6=11

Answer 1

To solve the equation |x| + 6 = 11, we will isolate the absolute value term.

First, subtract 6 from both sides of the equation:
|x| = 11 - 6
|x| = 5

Since the absolute value of x is 5, this means that x is either 5 or -5.

To graph the solution, plot the points (5,0) and (-5,0) on a number line.

Checking the solutions:
For x = 5, substituting into the original equation, we get:
|5| + 6 = 11
5 + 6 = 11
11 = 11 (true)

For x = -5, substituting into the original equation, we get:
|-5| + 6 = 11
5 + 6 = 11
11 = 11 (true)

Therefore, the solutions to the equation are x = 5 and x = -5.