How do you solve abs(1/2x+4)=6∣∣∣12x+4∣∣∣=6?

1 Answer
smendyka
Mar 21, 2018

See a solution process below:

Explanation:

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:

1/2x + 4 = -612x+4=−6

1/2x + 4 - color(red)(4) = -6 - color(red)(4)12x+4−4=−6−4

1/2x + 0 = -1012x+0=−10

1/2x = -1012x=−10

color(red)(2) xx 1/2x = color(red)(2) xx -102×12x=2×−10

color(red)(2)/2x = -2022x=−20

1x = -201x=−20

x = -20x=−20

Solution 2:

1/2x + 4 = 612x+4=6

1/2x + 4 - color(red)(4) = 6 - color(red)(4)12x+4−4=6−4

1/2x + 0 = 212x+0=2

1/2x = 212x=2

color(red)(2) xx 1/2x = color(red)(2) xx 22×12x=2×2

color(red)(2)/2x = 422x=4

1x = 41x=4

x = 4x=4

The Solution Set Is: x = {-20, 4}x={−20,4}

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