healingduck said:
That's kind of the part I'm confused about. Common sense would tell
me to move the one to the 5 so it would read -x<6
That is *one* of the correct routes.
You need to get x on one side by itself.
\(\displaystyle -x \ < \ 6\)
When you multiply or divide each side of an inequality
by a negative number, then the sign changes in *that*
step.
The following is wrong:
\(\displaystyle (-1)(-x) \ < \ (-1)(6)\)
\(\displaystyle x \ > \ -6\)
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And so, too, is the following wrong:
\(\displaystyle \frac{-x}{-1} \ < \ \frac{6}{-1}\)
\(\displaystyle x \ > \ -6\)
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Using the division option from the original problem,
it would be this:
\(\displaystyle -x \ < \ 6\)
\(\displaystyle \frac{-x}{-1} \ > \ \frac{6}{-1}\)
\(\displaystyle x \ > \ -6\)
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Or, you might want to avoid multiplying or
dividing by a negative number as in:
\(\displaystyle -x \ < \ 6\)
\(\displaystyle -x + (x - 6) \ < \ 6 + (x - 6)\)
\(\displaystyle -6 \ < \ x\)
Turning it around:
\(\displaystyle x \ > \ -6\)
