The perimeter of the Jacobs square backyard is no more than 72 meters.what is the solution set for the length that his backyard can be?

Question

What's the variable?

What's the inequality ?

whats the solution?

how do I graph this?

Answer 1

You are asking the right questions - you just need to think carefully to find the answers  

 

You are looking for the length of the backyard, so that's the variable.  Call it  X  for short  

 

The inequality requires a bit more thought.  You are told that the perimeter of the square backyard is no more than 72 meters.  But how is the perimeter of a square related to the length of a side of the square?  A square has 4 equal sides, so the perimeter is 4 times the length of a side.  That is, the perimeter = 4*X.  So if the perimeter is no more than 72 meters, then  4*X ≤ 72  is the inequality  

 

For the most part solving an inequality is very similar to solving an equation.  In this case you can just divide both sides by 4 to obtain the solution  X ≤ 18 .  Now there's one thing that isn't stated explicitly in the problem but you need to use a little common sense to figure out, and that's that you can't have a negative length for the backyard.  In fact, you can't have a zero length either (or else there would be no backyard!).  So you need to add the constraint that  X > 0 .  You can write the solution as a compound inequality  0 < X ≤ 18  

 

To graph this first draw a number line.  Then put an open circle at X = 0 (open because 0 is not included in the solution set) and a closed circle at X = 18 (closed or filled in because 18 is included in the solution set) and shade in everything on the number line between these 2 circles.  And that's it - the shaded part is the solution