How do you solve 3|x+11|=24?

1 Answer
smendyka
Sep 28, 2017

See a solution process below:

Explanation:

First, divide each side of the equation by color(red)(3) to isolate the absolute value function while keeping the equation balanced:

(3abs(x + 11))/color(red)(3) = 24/color(red)(3)

(color(red)(cancel(color(black)(3)))abs(x + 11))/cancel(color(red)(3)) = 8

abs(x + 11) = 8

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

x + 11 = -8

x + 11 - color(red)(11) = -8 - color(red)(11)

x + 0 = -19

x = -19

Solution 2:

x + 11 = 8

x + 11 - color(red)(11) = 8 - color(red)(11)

x + 0 = -3

x = -3

The Solutions Are: x = -19 and x = -3

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