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How do you solve #7| x + 3| = 21#?

Answer 1

See the solution process below:

First, divide each side of the equation by #color(red)(7)# to isolate the absolute value function while keeping the equation balanced:

#(7abs(x + 3))/color(red)(7) = 21/color(red)(7)#

#(color(red)(cancel(color(black)(7)))abs(x + 3))/cancel(color(red)(7)) = 3#

#abs(x + 3) = 3#

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1)

#x + 3 = -3#

#x + 3 - color(red)(3) = -3 - color(red)(3)#

#x + 0 = -6#

#x = -6#

Solution 2)

#x + 3 = 3#

#x + 3 - color(red)(3) = 3 - color(red)(3)#

#x + 0 = 0#

#x = 0#

The solution is: #x = -6# and #x = 0#

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Answer 2

Isaiah Anthony

#x=0 or x=-6#

Begin by dividing by #7# on both sides:

#cancel(7/7)|x+3|=21/7 -> |x+3|=3#

Set up the two stipulations and solve for #x#:

#color(blue)(x+3=3)#

#color(blue)(x+cancel(3-3)=3-3)#

#color(blue)(x=0)#

----------------------------------------------#or#----------------------------------------------

#color(red)(x+3=-3)#

#color(red)(x+cancel(3-3)=-3-3)#

#color(red)(x=-6)#

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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.