Write and solve an equation for each situation. Check your solution. See Problem 2.- Architecture An architect is designing a rectangular
greenhouse. Along one wall is a 7-ft storage area
an d 5 sections for different kinds of plants. On the
opposite wall is a 4-ft storage area an d 6 sections
for plants. All of th e sections for plants are of equal
length. W hat is the length of each wall? - Business A hairdresser is deciding w here to
o p en h er own studio. If the h airdresser chooses
Location A, she will pay $1200 p er m o n th in rent a n d will charge $45 p er haircut.
If she chooses Location B, she will pay $1800 p er m o n th in rent a n d will charge
$60 p er haircut. How m any haircuts w ould she have to give in one m o n th to m ake
th e sam e profit at either location?
Solve each equation. Check your answer. See Problem 3.- 3(<? — 5) = 2(<7 + 5) 22. 8 - ( 3 + b) = b - 9
- 7(6 - 2a) = 5(-3a +1) 24. (g + 4) - 3g = 1 + g
- 2r - (5 - r) = 13 + 2r 26. 5 g + 4 (—5 + 3g) = 1 - g
Determine whether each equation is an identity or w hether it has no sol ut i on. See Problem 4.
5 y + 2 = |(1 0 y + 4)
2(2k - 1) = 4(ifc - 2)
4 - d = —( d - 4)identity. If it has no
3d + 4 = 2 + 3d - 1
3a + 1 = —3 .6 (a - 1)0.5b + 4 = 2{b + 2)
3 (m + 1.5) = 1.5(2m + 3)- Travel Suppose a family drives at an average rate of 60 m i / h on th e way to visit
relatives a n d th e n at an average rate of 40 m i / h on th e way back. The re tu rn trip
takes 1 h longer th a n the trip there.
a. Let d be th e distance in m iles th e family traveled to visit th eir relatives. How
m any hours did it take to drive there?
b. In term s of d, how m any h ours did it take to m ake th e re tu rn trip?
c. Write an d solve an equ atio n to d eterm in e th e distance th e family drove to see
th eir relatives. W hat was th e average rate for th e entire trip? - 2 (a - 4) = 4a - (2a + 4) 28.
- k - 3k= 6k + 5 - 8k 3 0.
- 6 a + 3 = - 3 ( 2 a - 1) 32.
^ Apply Solve each equation. If the equation is an identity, write
solution, write no sol ut i on.- 3.2 - 4d= 2.3d + 3 34.
- 2.25(4x - 4) = - 2 + lOx + 12 36.
- \h + |(b - 6) = |b + 2 38.
- 2 ( - c - 12) = - 2 c - 12 40.
106 Chapter 2 So l v i n g Eq u a t i o n s