How do you solve abs(4x-7)=13?

1 Answer
smendyka
Aug 22, 2017

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:

4x - 7 = -13

4x - 7 + color(red)(7) = -13 + color(red)(7)

4x - 0 = -6

4x = -6

(4x)/color(red)(4) = -6/color(red)(4)

(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -6/4

x = -3/2

Solution 2:

4x - 7 = 13

4x - 7 + color(red)(7) = 13 + color(red)(7)

4x - 0 = 20

4x = 20

(4x)/color(red)(4) = 20/color(red)(4)

(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 5

x = 5

The Solutions Are: x = -3/2 and x = 5

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