How Do You Solve an AND Compound Inequality?

s is the variable we are trying to solve for in this compound inequality
If you're stuck with compound inequalities, just split them up!
The addition property of inequality lets us isolate '7s' by adding 200 to each inequality
The division property of inequality lets us solve for 's'
We can write the answer with set builder notation

1. We have two inequality symbols and no absolute value signs, that's how we know that there are really 2 inequalities to work with here
1. The steps for solving these inequalities are identical, that's why it's best to solve them side by side
1. The addition property of inequality tells us that if we add 200 to one side of the inequality, then we have to add 200 to the other side of the inequality too!
1. The addition property of inequality tells us that if we add 200 to one side of the inequality, then we have to add 200 to the other side of the inequality too!
2. -200 + 200 = 0, that's why '7s' is left alone
1. The division property of inequality lets us isolate 's' by dividing both sides of each simplified inequality by 7
1. The division property of inequality tells us that if we divide both sides of an inequality by a negative number then we have to FLIP the inequality around!
2. In this case we don't have to flip anything :)
1. Dividing 609 by 7 is harder to do in your head, so long division might be a better choice if you don't have a calculator handy!
1. Remember that the problem started out as a one line inequality (430>7s-200≥409)
1. Set builder notation can be used to write any compound inequality you come across!

Solve this inequality for s:430>7s-200≥409