I don't understand how to solve this problem.
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2 Answers

-3x > 3x+6

0 > 6x+6

-6 > 6x

6x < -6

This is an inequality and you solve it as if it were an ordinary equation with equals (an equality) instead of greater than (>). Collect the knowns on one side of the inequality and the unknowns on the other. When you cross over the > sign remember to convert + to - and - to plus. So to minimise the negatives, take the z's over to the right: 0>6+6z. You can turn this round first if you like, but you have to reverse the inequality to keep it true. 6+6z<0. That simply says, if something is less than something else, then that something else must be greater than that something, or vice versa. Take 6 across the inequality so that it becomes -6: 6z<-6. Divide both sides by 6: z<-1. If you have problems thinking in negatives, use a thermometer as a guide. Degrees above zero are positive, degrees below zero are negative. If z were a temperature then z must be less than 1 degree below zero, i.e., cooler. 6 times cooler than this would be -6. 6 degrees warmer would mean we add 6. It sometimes helps to use something we can easily understand to grasp mathematical concepts.

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