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.
If there is any unknown value in the given verbal phrase, replace it by some English alphabet.
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
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 + 2mn2 = 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 + y2 = 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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