Evaluating Algebraic Expressions

Two-Variable Expressions

1

3(y + x) ; use x = 4, y = 0

3(4) = 12

2

4 + xy ; use x = 7 and y = 3

4 + 21 = 25

3

8(5 - x) - y ; use x = 3 and y = 12

8(5 - 3) - 12 = 8(2) - 12 = 16 - 12 = 4

4

(c + d) + 4(c) ; use c = 8, d = 9

(8 + 9) - 4(8) = 17 + 32 = 49

5

5(f - h) - 2h ; use h = –1, f = 2

5(2 - -1) - 2(-1) = 5(2 + 1) + 2 = 5(3) + 2 = 17

Expressions with Exponents

1

3x²-17 ; x=5

58

2

9²-x³ ; x=4

17

3

10(x²); when x = 2

40

4

x³ + x + 5; when x = 3

35

5

a² + b² + c² ; when a = 1. b = 4, and c = 6

53

One-Variable Expressions

1

4(x) ; x = 12

48

2

3y ; use y =3

9

3

t÷18 ; t = 0

0

4

(5y - y)÷2 ; y = 6

(30 - 6)/2 = 24/2 = 12

5

(50 + g)÷g ; g = 10

6

(Similar to) Sam's Diner

1

At the diner, I ordered a sandwich (S) and a drink (D). 

The sandwich costs 5.50 and the drink costs 1.00

I order the same thing for my friend to-go, which can be represented by the expression:

2(S + D)

How much money did I spend in total?

$13

2

At the bookstore, I bought a notebook (N) and a pen (P).

• The notebook costs $3.00, and the pen costs $1.50.

I bought the same items for my friend as well, represented by the expression:

2(N + P)

How much money did I spend in total?

$9.00

3

At the game store, I bought a game (G) and a controller (C).

• The game costs $15.00, and the controller costs $25.00.

I bought another game and controller as a gift for my cousin, which can be represented by the expression:

2(G + C)

How much money did I spend in total?

$80.00

4

At the sports store, I bought a soccer ball (B) and a pair of cleats (C).

• The soccer ball costs $20.00, and the cleats cost $45.00.

I bought these same items again for my sibling, represented by the expression:

2(B + C)

How much did I spend in total?

$130.00

5

At the craft shop, I bought a sketchbook (K) and a set of paints (P).

• The sketchbook costs $12.50, and the paint set costs $18.00.

I decided to buy another sketchbook and paint set for a friend, which can be represented by the expression:

2(K + P)

How much did I spend altogether?

$61.00