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

2 Answers
smendyka
Nov 7, 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:

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

Rhys
Nov 7, 2017

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}

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