How do you graph and solve |5x – 2|>=8?

1 Answer
smendyka
Jul 27, 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.

Therefore we can write and solve this as:

-8 >= 5x - 2 >= 8

First, add color(red)(2) to each segment of the system of inequalities to isolate the x term while keeping the system balanced:

-8 + color(red)(2) >= 5x - 2 + color(red)(2) >= 8 + color(red)(2)

-6 >= 5x - 0 >= 10

-6 >= 5x >= 10

Now, divide each segment by color(red)(5) to solve for x while keeping the system balanced:

-6/color(red)(5) >= (5x)/color(red)(5) >= 10/color(red)(5)

-6/5 >= (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) >= 2

-6/5 >= x >= 2

Or

x <= -6/5; x >= 2

Or

(-oo, -6/5]; [2. +oo)

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