word problem

Question

drew and Mat are arm-wrestling. Mat is stronger than drew, but drew is young and crafty. He knows that if 4 multiplied by the time they arm-wrestle,t, is greater than 4 but less than or equal to 16,he has a chance at winning. Write a compound inequality and solve for t. then grapph your solution on a number li

Answer 1

4 <  4t <= 16

 

1 < t <= 4 <--- divides all three sides by 4

 

open circle at 1, closed circle at 4. shade in between

 

Drew must pin Mat within 4 seconds or else he will lose.

Answer 2

So drew will win if both inequalities are true:

1. 4t > 4,   or 4 < 4t
2. 4t ≤ 16, or 16 ≥ 4t

Note how you can write the inequalities in either direction as long as you have the inequality "alligator" eating the larger side.

 

Since both inequalities involve 4t, make that one in the middle. It's also preferred when combining them that we go left to right from smallest side to largest side. So we end up with this:

 

4 < 4t         4t ≤ 16

      4 < 4t ≤ 16

      1 < t ≤ 4                  , after we divide all three "sides" to solve for t

 

When graphing this on the number line, you want an open circle (not shaded in) on 1 and a closed circle (shaded in) on 4.

• The closed circle shows that t is allowed to equal 4 (along with less than) 
• The open circle shows that t is not allowed to equal 1, only be greater than it

Connect the two circles to indicate all the values in between 1 & 4 that the time they're arm-wrestling can be in order for drew to beat Mat. Hope this helps!