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I am learning Algebra on Khan Academy and have a question on solving equations with variables on both sides that I know is basic but can't seem to find the answer to, so hoping someone could clarify.

Given the following equation and solving for $h$;

$$17+4h+2=1-5h$$

My first step is to combine the like terms, so $17+2$;

$$19+4h=1-5h \tag1$$

Now for the second step, I want to eliminate the variable on one side. I have two options and can get rid of the $5h$ or $4h$. Most advice online point to targeting the smallest number first ($4h$);

$$19+4h-4h=1 - 5h - 4h \tag2$$ $$19=1-1h \tag3$$

However that appears incorrect and the correct answer according to Khan Academy is $-2$. They have opted to eliminate the $5h$ instead;

$$19+4h=1-5h \tag4$$ $$19+9h=1 \tag5$$ $$9h=-18 \tag6$$ $$h=\frac{-18}{9} \tag7$$ $$h=-2 \tag8$$

Both answers appear correct ($h=18$ and $h=-2$).

Why would $h=18$ be incorrect? Is this an error with Khan Academy or am I missing something?

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2 Answers 2

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I've figured out my error, $1-5h-4h$ is not $1-1h$ but $1-9h$. It then resolves $h=-2$!

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"Both answers appear correct": in such cases, verify the answer !

$$17+4(-2)+2=1−5(-2)\equiv11=11$$

and

$$17+4\cdot18+2=1−5\cdot18\not\equiv91=-89.$$

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