| Variables and Constants |

Nov. 28, 2024, 6:35 p.m.

Definition

 

Variable

-> a quantity whose value may change during a given discussion or problem.

-> It is denoted usually by the last alphabetical letter such as x, y and z.

 

Constants

-> a quantity whose value is fixed during a given discussion or problem.

-> It is denoted fixed values such as 3, 5 , 7, etc.

 

Absolute Value

-> It is indicated by inclosing the constant by two vertical parallel lines.

-> It is denoted by | |.

 

Range of a variable

-> those are the values that may be given to the variable and will depend on the particular problem or discussion.

 

Example

 

1. Find the answer from this given:

| -3 |

 

Steps:

a. Inverse the input.

b. Compute.

= | -3 |

= 3

  1.  

Exercises

 

1. Find the answer from this given: |-7|.

Steps:

a. Inverse the input.

b. Compute.

 

Solution:

= |-7|

= 7

 

Answer: 7

2. Find the answer from this given: |x - 3| = 5.

Steps:

a. Inverse the input.

b. Interchange.

c. Compute.

 

Solution:

= |x - 3| = 5

= x - 3 = 5; x = 5 + 3

= 8

 

Answer: 8

3. Find the answer from this given: 2x + 5, if x = 3.

Steps:

a. Substitute the x.

b. Compute.

 

Solution:

= 2x + 5

= 2(3) + 5

= 11

 

Answer: 11

4. Find the answer from this given: y = 3x + 2, if x is equal to 1 & 4.

Steps:

a. Substitute the x.

b. Compute.

 

Solution:

= y = 3x + 2; if x = 1

= y = 3(1) + 2

= 5

 

= y = 3x + 2; if x = 4

= y = 3(4) + 2

= 14

 

= y [5,14]

 

Answer: y [5,14]

5. Find the answer from this given: x2 + C, if C = 7 & x = 2.

Steps:

a. Substitute the x and C.

b. Compute.

 

Solution:

= x2 + C

= (4) + 7

= 11

 

Answer: 11