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7.

8

2x = 2

8.

x + 10 = 2(x

6)

8

2x+2x

=

2+2x

x +

10+12

= 2x

12+12

8

2

= 2 + 2x

2

x + 22

x

= 2x

x

6

2x

22 = x

=

2

2

Matt is 22.

3 = x

Exercises IV

Solve for x. Show all of your steps.

(a) x + 3 = 2

(b) 2

x =

3

(c)

3x + 7 =

8

x

(d)

+ 5 = 7

10

(e) 2

x + 8

y =

x + y + 3

2

x

10

9

(f)

+ 1 =

x

4

Solving Systems of Equations

Amanda has two fair options at the toy shop.

(1) She can buy one deck of Pok´ e mon cards and one Rubik’s Cube for $20.

(2) Or for $7, she can buy two decks of Pok´ e mon cards but she also has to trade in the

Rubik’s Cube she has at home.

What are the prices of a deck of Pok´ e mon cards and a Rubik’s Cube?

How can you solve this problem?

Notice that we have two unknowns: the price of a deck of Pok´ e mon cards (x) and the price

of a Rubik’s Cube (y). We also have two diﬀerent options that can be represented by two

diﬀerent equations:

(1) one deck + one cube = $20. Mathematically, 1x + 1y = 20.

(2) two decks = $7 + one cube. Mathematically, 2x = 7 + 1y or 2x

1y = 7.

The goal in this situation is to ﬁnd x and y such that both equations are satisﬁed.

A System of Equations is a set of multiple equations dealing with multiple variables. You

have to work with all of the equations at the same time in order to solve for the variables.

7

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