Question

How do you solve `abs(2x+1)=5`?

Answer 1

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:

`2x + 1 = -5`

`2x + 1 - color(red)(1) = -5 - color(red)(1)`

`2x + 0 = -6`

`2x = -6`

`(2x)/color(red)(2) = -6/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -3`

`x = -3`

Solution 2:

`2x + 1 = 5`

`2x + 1 - color(red)(1) = 5 - color(red)(1)`

`2x + 0 = 4`

`2x = 4`

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

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 2`

`x = 2`

The Solutions Are: `x = -3` and `x = 2`

Answer 2

`x = {2,-3}`

Explanation:

We can tackle this by considering how `|a| = |-a|`

So hence;

`|-(2x+1)| = |2x+1| = 5`

So hence, `2x+1 = 5`
But also `-(2x+1) = 5`

As `|-(2x+1)| = |2x+1|`

So hence solving both linear equations we yield;

`x = {2,-3}`