Fraction two thirds is greater than z over five
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We can cross-multiply without upsetting the inequality provided we use positive numbers: -10>3z. We can divide both sides by 3: -10/3>z. We can switch the inequality around: z<-10/3. This means that z can be any value strictly less than -3 1/3. To prove we have the right answer, let's put z=-5, which is less (more negative) than -3 1/3: -2/3>-1. This is true because -2/3 is not as negative as -1, so it's bigger. Put z=0 which is bigger than -3 1/3 and we get -2/3>0, which is false and is the answer we would expect because we picked an invalid value for z.

by Top Rated User (711k points)

Given -2/3 > z/5
3z+10<0
3z<-10
3z<-10/3

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by Level 8 User (30.1k points)

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