Algebra 1 Common Core Student Edition, Grade 8-9

Lesso n Ch eck

Do y o u k n o w H OW?

Solve each equation. Check your answer.

1.5*+12 = - 1 3 2. 6 = y - 3

3. y — i-^ = -2 4. -* -4 = 9


4. Fundraising The ju n io r class is selling granola bars to
   raise m oney. They p u rc h ased 1250 granola bars an d
   paid a delivery fee of $25. The total cost, including
   the delivery fee, was $800. W hat was th e cost of each
   granola bar?

Do y o u UN DERSTAN D? @ PRACTICES

What properties of equality would you use to solve each

equation? What operation would you perform first?

Explain.

6. - 8 = | + 3 7. 2*-9 = 7

8. | - 8 = 4 9. -4* +3 = -5

(j^ 10. Reasoning Can you solve the eq u a tio n = 6 by

adding 3 before m ultiplying by 5? Explain.

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

Practice Solve each equation. Check your answer.

11. 2 + |= -1

15. 4b + 6 = —2


16. 26 = t? + 5
    12. 3n — 4 = 11
    16. 10 = f - 8
    20. 18 = 2

MATHEMATICAL

PRACTICES

13. -1 = 7 + 8 *


14. 10 + | = 1


15. -5 * -2 = 13

See Problem 1.

6 5

Define a variable and write an equation for each situation. Then solve.

23. Maximum Capacity A delivery p e rso n uses a service elevator to b ring boxes of
    books up to an office. The delivery p e rso n weighs 160 lb a n d each box of books
    weighs 50 lb. The m axim um capacity of th e elevator is 1000 lb. H ow m any boxes of
    books can th e delivery perso n bring u p at one time?


24. Shopping You have $16 an d a c o u p o n for a $5 d isco u n t at a local superm arket.
    A bottle of olive oil costs $7. How m any bottles of olive oil can you buy?


25. Rentals Two college friends rent an ap artm en t. They have to pay th e landlord
    two m o n th s' re n t a n d a $500 security deposit w h en they sign th e lease. The total
    a m o u n t they pay th e landlord is $2800. W hat is th e rent for one m onth?
    14. | + 2 =-8
    18. - 1 4 = - 5 + 3c
    22. 14= -2 k+3

See Problem 2.

Solve each equation. Check your answer.

26.

y-4

10 27. 7 =* —^8

30. 7‘2^1 * + 3 2 31. ^ 5 = -1

Solve each equation. Justify each step.

34. 14- b= 19 35. 20-3 b = 2

28.

32.

z+ 10

9

-2

2

d-7

36. 3 * 2 '

29.4 =

33.^-

See Problem 3.

a + 10

2

3 _ 5

3

See Problem 4.

37. -l= 4 + f

L

P o w e r A lg e b r a .c o m ^ | Lesson 2-2 So l v i n g Tw o - St e p Eq u a t i o n s 91