Solving an Absolute Value Equation

Learn how to solve absolute value equations with multiple steps. Absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value equation where there are more terms apart from the absolute value term in the same side of the equality sign as the absolute value term, we first isolate the absolute value term. i.e. make the absolute value term the subject of the formular.
After isolating the absolute value term, we now separate the equation into the positive and the negative cases and then solve accordingly.
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[@alexandery8508]

What if the equation equals a negative value?

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Is there a reason why we subtracted the 4 out first? Why not divide 26 by 3 first at 0.56?

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[@tubeprincessamirahtv7993]

Do you divide by three because you are trying to get rid of the three, at 0.49? You would multiply if there was a fraction?

[@brianmclogan]

correct

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So what do we write as our answer

[@brianmclogan]

x=2 and -18

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What if the equation equals a negative value?

[@brianmclogan]

No real solutions

[@Shaml1912]

If the absolute value is multiplied by (-) what i will do can you answer plz i have an exam

[@brianmclogan]

you have to isolate the abs sign so divide by -1 on both sides before creating your two cases

[@Shaml1912]

Thanks alot

[@brianmclogan]

you are very welcome!

[@vanjaa07]

how come you didn't split them into x+8= 10 and x-8=10 and then solve for them? why was the 10 as a -10 in the split equation?

[@brianmclogan]

Vanja Knezevic tough to explain in comment but remember if we don't know the value of x within an absolute value then absx =x and absx=-x so we negate the other side of the equation not within the abs

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[@paulsnyder1783]

Why are we not adding 4 to the 3?

[@manuellarios6989]

I understand how he got x+8=10 for the first part but for the second he put x+8=-10. Shouldn’t it be x minus 8 instead of x plus 8?
Edit: I figured it out, I just did more examples

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Holy fuuck. I accidentally multiplied the first number to both sides in my quiz i am freaking dead

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[@brianmclogan]

best of luck, practice, practice, practice

[@angelahjames7500]

Why did u start by adding the 4 to 26 instead of dividing 26 by 3

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Because that's not how u are suppose to start and plus u cant even divide 26 with 3 it gives u a decimal

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Quick maff. -10-8=-16;))))

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Wait how does 3÷3=0

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whats 56/8

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Sorry when did -10-8=16 I clicked off lol

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My teacher couldnt explain it to me