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How do you solve #abs(4w - 1) = 5w + 37#?

Answer 1

Hazel Anglin

#w=-4#

#abs(4w-1)=5w+37#

Separate the equation into a positive equation and a negative equation.

#4w-1=5w+37# and #-(4w-1)=5w+37#

Positive equation

#4w-1=5w+37#

Add #1# to both sides.

#4w=5w+38#

Subtract #5w# from both sides.

#4w-5w=38#

#-w=38#

Multiply both sides times #-1#.

#w=-38#

Check.

#abs(4*-38-1)=5*-38+37# =

#abs(-152)!=-153#

#152!=-153#

#w!=-38#

Negative equation

#-(4w-1)=5w+37# =

#-4w+1=5w+37#

Subtract #1# from both sides.

#-4w=5w+36#

Subtract #5w# from both sides

#-4w-5w=36#

#-9w=36#

Divide both sides by #-9#.

#w=36/(-9)=-4#

#w=-4#

Check.

#abs(4*-4-1)=5*-4+37# =

#abs(-17)=-20+37# =

#17=17#

#w=-4# checks.

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Answer 2

Eva Abramson

To solve the equation abs(4w - 1) = 5w + 37, you need to consider two cases: when 4w - 1 is positive and when it's negative.

When 4w - 1 is positive, the equation becomes 4w - 1 = 5w + 37. Solve for w.
When 4w - 1 is negative, the equation becomes -(4w - 1) = 5w + 37. Solve for w. After finding the solutions for both cases, check if they satisfy the original equation.

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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.