negative 24 less than or equal to negative 8x

Question

Math homework, need some help.

Answer 1

-24<-8x. We can't simply cancel the negatives when we have an inequality. But we can add and subtract quantities from each side without violating the inequality, so add 24 to each side: 0<-8x+24. Now add 8x to both sides: 8x<24, and divide both sides by 8: x<3. We can divide or multiply by a positive number without violating the inequality.