EVALUATING ALGEBRAIC EXPRESSIONS

Recall that an algebraic expression contains one or more variables. We can substitute a number for each variable and then find the value of the expression.

This process is called evaluating the expression.

For example, to evaluate 2m for m = 5, we would plug 5 for m.

2m = 2(5) = 10

Parentheses are another way to show multiplication. 

2(5) = 2 × 5 = 10

Example 1 :

Evaluate the expression for the given value of the variable.

x - 9; x = 15

Solution :

15 - 9 = 6

Therefore, when x = 15, x - 9 = 6.

Example 2 :

Evaluate the expression for the given value of the variable.

16/n; n = 8

Solution :

16/8 = 2

Therefore, when n  =  8, 16/n = 2.

Example 3 :

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

3x + 2y

Solution :

Substitute x = 3 and y = 5 in the given expression

= 3(3) + 2(5)

 = 9 + 10

= 19

Therefore, 3x + 2y = 19.

Example 4 :

Evaluate the given expression for y = 1.4. 

0.5y

Solution :

Substitute y = 1.4 in the given expression

= 0.5(1.4)  

= 0.5 x 1.4 

= 0.7

Therefore, 0.5y = 0.7.

Example 5 :

Evaluate the given expression for s = 5. 

s2 + 7s - 2

Solution :

Substitute s = 5 in the given expression

= 52 + 7(5) - 2  

= 25 + 35 - 2  

= 58

Therefore, s² + 7s - 2 = 58.

Example 6 :

Evaluate the given expression for m = 1/3. 

18m2 + 3m + 7

Solution :

Substitute m = 1/3 in the given expression

= 18(1/3)2 + 3(1/3) + 7  

= 2 + 1 + 7  

= 10

Therefore, 18m² + 3m + 7 = 10.

Example 7 :

Evaluate the given expression for m = 13. 

m+ m - 54

Solution :

Substitute m = 13 in the given expression.

= 132 + 13 -54  

= 169 + 13 - 54  

= 128

Therefore, m2 + m - 54 = 128.

Example 8 :

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

x2 + y2

Solution :

Substitute x = 3 and y = 5 in the given expression.

= 32 + 52  

= 9 + 25  

= 34

Therefore, x2 + y2 = 34.

Example 9 :

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

5m2 + 2m2n

Solution :

Substitute m = 5 and n = 2 in the given expression.

= 5(5)2 + 2(5)2(2)  

= 125 + 100 

= 225

Therefore, 5m2 + 2m2n = 225.

Example 10 :

Evaluate the given expression for m = 3. 

(2m2 + 5m - 7)/2

Solution :

Substitute m = 3 in the given expression

= [2(3)2 + 5(3) - 7]/2

 = [18 + 15 - 7]/2

= 26/2

 = 13

Therefore, (2m2 + 5m - 7)/2 = 13.

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