Algebra 1 Mid-Term Study Guide Help

Question

Hey, I have to take mid-terms next week for my Algebra 1 class and I just wanted to ask for some help. The questions are from the study quide i was given and didn't get to ask how to do them. Sorry if some of these seem stupidly easy, it is just the ones that I had the most problem with so I thought I would ask for some explanation to learn what I did wrong.Here they are:

1. One side of a triangle has length 12cm and the second side is 3 cm longer than the third side. Find the lengths if the perimeter is 72cm.

2. The sum of twice a number and -6 is 9 more than the opposite of the number. Find the number.

3. . Dave and Daniel leave their houses at 9:30AM walking toward each other. They meet at 10:00AM. If their houses are 8km apart, and Dave is
walking at 9km/h, find Daniel’s rate.

Answer 1

1) x=third side

    x+3=second side

      12=first side

    72=x+x+3+12

    72=2x+15

    72-15=2x

    57=2x

    x=57/2

    x=28.5 cm

    x+3=31.5 cm

    check: 31.5+28.5+12=72

 

2) 2x+(-6)=-x+9

    2x+x=6+9

    3x=15

      x=5

 

3) d=r*t

    8=9(1/2)+r(1/2)   ( 9:30 to 10:00 is 1/2 an hour)

    8=4.5+0.5r

    8-4.5=0.5r

    3.5=0.5r

    35=5r

    r=35/5

    r=7 km/h