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How do you solve #abs(15-2x)=8#?

Answer 1

Kennedy Adams

#x=7/2" or " x=23/2#

This kind of equation has two possible answers.

Eliminating the 'bars' provides.

#15-2x=color(red)(+-)8#

#• " solve " 15-2x=color(red)(+)8#

Add 15 to each side.

#cancel(15)cancel(-15)-2x=8-15#

#rArr-2x=-7#

split each side by -2.

#(cancel(-2) x)/cancel(-2)=(-7)/(-2)#

#rArrx=7/2#

#• " solve " 15-2x=color(red)(-)8#

#rArr-2x=-23#

#rArrx=23/2#

#color(blue)"As a check"#

These values are the solutions if you substitute them into the left side of the equation and see if they equal the right side.

#|15-2xx7/2|=|8|=8#

#|15-2xx23/2|=|-8|=8#

#rArrx=7/2" or " x=23/2" are the solutions"#

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Answer 2

Jameson Allen

To solve the equation |15 - 2x| = 8:

Split the equation into two cases: Case 1: 15 - 2x ≥ 0 Case 2: 15 - 2x < 0
For Case 1: 15 - 2x = 8 Solve for x: -2x = 8 - 15 -2x = -7 x = -7/-2 x = 7/2
For Case 2: -(15 - 2x) = 8 Solve for x: -15 + 2x = 8 2x = 8 + 15 2x = 23 x = 23/2
Check the solutions in the original equation to ensure they are valid.
The solutions to the equation are x = 7/2 and x = 23/2.

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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.