**Using the order of operations :**

Algebraic expressions may have more than one operation or more than one variable. To evaluate these expressions, substitute the given value for each variable and then use the order of operations.

**Example 1 :**

Evaluate the given expression for x = 7.

4(x - 4)

**Solution : **

Plug 7 for x

4(7 - 4)

Subtract inside the parentheses

4(3)

Multiply

12

Therefore, 4(x - 4) = 12.

**Example 2 :**

Evaluate the given expression for x = 7.

4x - 4

**Solution : **

Plug 7 for x

4(7) - 4

Multiply

28 - 4

Subtract

24

Therefore, 4x - 4 = 24.

**Example 3 :**

Evaluate the given expression for w = 6, x = 5 and y = 3.

w - x + y

**Solution : **

Plug 6 for w, 5 for x and 3 for y

6 - 5 + 3

Subtract 5 from 6

1 + 3

Add 1 and 3

4

Therefore, w - x + y = 4.

**Example 4 :**

Evaluate the given expression for x = 9.

x² - x

**Solution : **

Plug 9 for each x

9² - 9

Evaluate exponents

81 - 9

Subtract

72

Therefore, x² - x = 72.

**Example 5 :**

Evaluate the given expression for x = 3 and y = 5.

3x + 2y

**Answer :**

Plug 3 for x and 5 for y

3(3) + 2(5)

Multiply

9 + 10

Add

19

Therefore, 3x + 2y = 19

**Example 6 :**

Evaluate the given expression for s = 5.

s² + 7s - 2

**Answer :**

Plug 5 for each s

5² + 7(5) - 2

Evaluate exponents

25 + 7(5) - 2

Multiply 7 and 5

25 + 35 - 2

Add 25 and 35

60 - 2

Subtract 2 from 60

58

Therefore, s² + 7s - 2 = 58

**Example 7 :**

Evaluate the given expression for m = 5 and n = 2.

m² + 2mn²

**Answer :**

Plug 5 for m and 2 for n

5² + 2(5)(2)²

Evaluate the exponents

25 + 2(5)(4)

Multiply

25 + 40

Add

65

**Example 8 :**

Evaluate the given expression for m = 3.

(2m² + 5m - 7) / 2

**Answer :**

Plug 3 for each m

[2(3)² + 5(3) - 7] / 2

Evaluate the exponents

[2(9) + 5(3) - 7] / 2

Multiply

[18 + 15 - 7] / 2

Add 18 and 15

[33 - 7] / 2

Subtract 7 from 33

26 / 2

Divide

13

Therefore, (2m² + 5m - 7)/2 = 13

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