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How do you solve #|5x + 11| = 6#?

Answer 1

See a solution process below: #x = -17/5# and #x = -1#

Since the absolute value function takes any term and converts it to a non-negative form, we have to solve the term for both its positive and negative equivalent within the absolute value function.

First Solution:

#5x + 11 = -6#

#5x + 11 - color(red)(11) = -6 - color(red)(11) #

#5x + 0 = -17#

#5x = -17#

#(5x)/color(red)(5) = -17/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -17/5#

#x = -17/5#

Option 2:

#5x + 11 = 6#

#5x + 11 - color(red)(11) = 6 - color(red)(11) #

#5x + 0 = -5#

#5x = -5#

#(5x)/color(red)(5) = -5/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -1#

#x = -1#

The Solutions Are: #x = -17/5# and #x = -1#

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Answer 2

Eva Abramson

To solve ( |5x + 11| = 6 ), you set up two equations:

( 5x + 11 = 6 )
( 5x + 11 = -6 )

Then, you solve each equation separately for x.

For ( 5x + 11 = 6 ): ( 5x = -5 ) ( x = -1 )
For ( 5x + 11 = -6 ): ( 5x = -17 ) ( x = -\frac{17}{5} )

So, the solutions are ( x = -1 ) and ( x = -\frac{17}{5} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.