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How do you solve #- 2abs(x - 3) + 10 = - 4#?

Answer 1

Eli Assouline

#x=10" or "x=-4#

Isolate the #color(blue)"absolute value"#

Deduct 10 from each side.

#-2|x-3|cancel(+10)cancel(-10)=-4-10#

#rArr-2|x-3|=-14#

split each side by -2.

#cancel(-2)/cancel(-2)|x-3|=(-14)/(-2)#

#rArr|x-3|=7larrcolor(red)"absolute value isolated on left"#

There are typically two solutions to equations with an absolute value.

We now solve #x-3=color(red)(+-)7#

#color(blue)"Solution 1"#

#x-3=color(red)(+)7rArrx=7+3=10#

#color(blue)"Solution 2"#

#x-3=color(red)(-)7rArrx=-7+3=-4#

#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.

#•x=10to-2|10-3|+10=-14+10=-4#

#•x=-4to-2|-4-3|+10=-14+10=-4#

#rArrx=10" or "x=-4" are the solutions"#

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Answer 2

Ethan Adkins

To solve the equation ( -2| x - 3| + 10 = -4 ), you would first isolate the absolute value expression by subtracting 10 from both sides, then divide both sides by -2. This gives you ( | x - 3| = 7 ). Then, you would consider the two cases: ( x - 3 = 7 ) and ( x - 3 = -7 ). Solving each case separately will give you the possible values for ( x ).

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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.