# WRITING AND EVALUATING EXPRESSIONS

In this section, you will learn how to write a mathematical expression from a verbal description and evaluate expressions for the given values of the variables or unknowns.

## Writing Expression from a Verbal Phrase

If there is any unknown value in the given verbal phrase, replace it by some English alphabet. ## Writing Expressions

In each case, write the given verbal phrase as mathematical expression.

Example 1 :

The sum of 5 times a number and 8

Solution :

5x + 8

Example 2 :

2 times the sum of 7 times a number and 4

Solution :

2(7x + 4)

Example 3 :

7 less than 4 times a number

Solution :

4x - 7

Example 4 :

One fifth of sum of 3 times a number and 9

Solution :

(3x + 9) / 5

Example 5 :

One seventh of 3 less than 4 times a number

Solution :

(4x - 3) / 7

Example 6 :

5 times of a number is decreased by 8

Solution :

5x - 8

Example 7 :

6 times of a number is increased by 15

Solution :

6x + 15

Example 8 :

7 less than 3 times the sum of a number and 6

Solution :

3(x + 6) - 7

Example 9 :

3 times the difference between a number and 8

Solution :

3(x - 8)

Example 10 :

One fourth of 3 times the difference between a number and 6

Solution :

3(x - 6) / 4

## Evaluating Expressions

Example 1 :

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

3x + 2y

Solution :

Substitute 3 for x and 5 for y into the given expression.

3x + 2y = 3(3) + 2(5)

= 9 + 10

= 19

Example 2 :

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

m2 + 2mn2

Solution :

Substitute 5 for m and 2 for n into the given expression.

m2 + 2mn= 52 + 2(5)(2)2

= 25 + 40

= 65

Example 3 :

Evaluate the following expression for s = 5.

s2 + 7s - 2

Solution :

Substitute 5 for s into the given expression.

s2 + 7s - 2 = 52 + 7(5) - 2

= 25 + 35 - 2

= 58

Example 4 :

Evaluate the following expression for m = 1/3.

18m2 + 3m + 7

Solution :

Substitute 1/3 for m into the given expression.

18m2 + 3m + 7 = 18(1/3)2 + 3(1/3) + 7

= 2 + 1 + 7

= 10

Example 5 :

Evaluate the following expression for m = 13.

m2 + m - 54

Solution :

Substitute 13 for s into the given expression.

m2 + m - 54 = 132 + 13 -54

= 169 + 13 - 54

= 128

Example 6 :

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

x2 + y2

Solution :

Substitute 3 for x and 5 for y into the given expression.

x2 + y= 32 + 52

= 9 + 25

= 34

Example 7 :

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

5m2 + 2m2n

Solution :

Substitute 5 for m and 2 for n into the given expression.

5m2 + 2m2n = 5(5)2 + 2(5)2(2)

5(25) + 2(25)(2)

= 125 + 100

= 225

Example 8 :

Evaluate the following expression for s = 6.

s2 - 3s + 10

Solution :

Substitute 6 for s into the given expression.

s2 - 3s + 10 = 62 - 3(6) + 10

= 36 - 18 + 10

= 28

Example 9 :

Evaluate the following expression for x = 2 and y = -5.

x2 - 3y2

Solution :

Substitute 2 for x and -5 for y into the given expression.

x2 - 3y2  =  2(2)2 - 3(-5)2

=  2(4) - 3(25)

= 8 - 75

= -77

Example 10 :

Evaluate the following expression for m = 3.

(2m2 + 5m - 7)/2

Solution :

Substitute 3 for m into the given expression.

(2m2 + 5m - 7)/2 = [2(3)2 + 5(3) - 7]/2

= [2(9) + 15 - 7]/2

= (18 + 15 - 7)/2

= 26/2

= 13

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