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Chapter 2: Q46. (page 66)

Evaluate the expression whenx=鈥�鈥�-5,鈥�鈥�y=3,鈥�鈥�and鈥�鈥�z=2.

2x鈥�鈥�+鈥�鈥�9y鈥�鈥�+鈥�鈥�5z

Short Answer

Expert verified

鈥�2x鈥�鈥�+鈥�鈥�9y鈥�鈥�+鈥�鈥�5z鈥�鈥�=鈥�鈥�27.

Step by step solution

01

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

02

Step-2 – Associative Property of Addition of Real Numbers: 

Suppose a, b, and c is three real numbers.

Associative property of Addition: (a + b) + c = a + (b + c)

If you are adding three real numbers, the sum is always the same regardless of their grouping.

Example: (11+12) + 13 = 11 + (12+13) = 36

03

Step-3 – Evaluate the expression

Associative property of Addition states, if you are adding three real numbers, the sum is always the same regardless of their grouping.

Evaluate the expression:

To evaluate the expression2x鈥�鈥�+鈥�鈥�9y鈥�鈥�+鈥�鈥�5z, substitute the value of x as 鈥� 5 and the value of y as 3 and z = 2 and addition of the numbers as shown below,

鈥夆赌夆赌夆赌夆赌夆赌夆赌�2x鈥夆赌�+鈥夆赌�9y鈥夆赌�+鈥夆赌�5z=鈥夆赌�2(鈭�5)鈥夆赌�+9鈥夆赌�(3)鈥夆赌�+5鈥夆赌�(2)鈥夆赌夆赌夆赌夆赌夆赌夆赌塖ubstitute鈥夆赌�x=鈭�5,鈥夆赌�y=3鈥夆赌塧nd鈥夆赌�z=2=鈥夆赌�鈭�鈥�10鈥夆赌�+鈥夆赌�27鈥夆赌�+鈥夆赌�10=鈥夆赌�(鈭�10+鈥�27)+10鈥夆赌夆赌夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆赌夆赌夆�夆赌�(Associative鈥夆赌塒roperty鈥夆赌塷f鈥夆赌堿ddition)=鈥夆赌�鈭�10鈥夆赌�+鈥夆赌�(27鈥夆赌�+鈥夆赌�10)鈥夆赌夆赌夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆赌夆赌夆�夆赌夆�夆赌�(Associative鈥夆赌塒roperty鈥夆赌塷f鈥夆赌堿ddition)=鈥夆赌�鈭�10+37=27

鈥�2x鈥夆赌�+鈥夆赌�9y鈥夆赌�+鈥夆赌�5z鈥夆赌�=鈥夆赌�27

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