Question

5x > 35
Answers to choose from
x = 7
x > 7
x < 7
x ≥ -7
x > -7


I was thinking it would be x > 7, am I right?

Answer 1

\[5x>35\]We can divide both sides of the inequality by 5, giving us:

\[\frac{5x}5 > \frac{35}5\]or\[x>7\]Therefore, you are correct.

You have to be careful when doing this as dividing (or multiplying) by a negative number reverses the direction of the inequality. For example, if we divided \(x>7\) by \(-1\), we get
\[\frac{x}{-1} < \frac{7}{-1}\]\[-x<-7\]If you draw the number line and mark where each inequality is true, it shouldn't be hard to convince yourself that the two are equivalent.