SLC-S22W1/Variables and Expressions

Hi guys, you are welcome to my blog. Without any delay, let's attend to the questions presented by @khursheedanwar, I hope it will be fun...

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• Task 1Explain any two variables and expressions types other than that which are explained in this course. (Practical and algebraic examples are required!)

To understand what a variable is, we must first understand what Algeria is. Algebra is a combination of digits or numbers and letters or symbols. When a number, say 4, is written together with a letter, say m; 4m, it is called algebra.

In mathematics, variables are often letters used to represent a value. They are also used to represent an unknown quantity, value, or relationship in mathematical function, equation, or expression. a and z in 6a + 3z - 4 are variables. Variables can be dependent, independent, or controlled.

An expression, on the other hand, is the collection and combination of mathematical operations, variables, and numbers to form a mathematical statement. Examples of expression include:
2(3y + 5) - 6, 7 - 2(3 - 1)

An expression can include numbers, also known as constants, variables, which can be letters or symbols that represent unknown values, and mathematical operations like +, -, ×, ÷, etc; it can also include functions like sin, log, cos, and exponents like 2y², X², 3².

An expression like 2 + 3(3 - 1) has multiple operations and makes use of parentheses in prioritizing and grouping the calculation. This type of expression is called a Nested or Compound Algebraic Expression.

An expression like 4y + 3x(2 - 1) has coefficients 4 and 3, variables y and x, involves primary mathematical operations +, -, ×, and doesn't have any non-linear term like X². Such a type of expression is called Linear Polynomial Algebraic Expression.

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• Task 2Show your way of evaluating of an algebraic expression if values of variables are given? Step by step explanation required! (The more you will be detailed and accurate, the more your task will be perfect!)

When evaluating an algebraic expression in which the value of the variable is given, the steps I will take are as follows:
Let's consider:
Evaluate -2x - 2(3x - 4) - x, where x = 2
Solution
Since the value of the variable X is given as 2,
Step 1: Substitute x for 2
-2(2) - 2(3(2) - 4) - 2
= -4 - 2(6 - 4) - 2
Step 2: Clear bracket; which is the first order of BODMAS.
= -4 - 12 + 8 - 2
Step 3: Following the order of BODMAS, we carry out addition before subtraction
= -4 - 4 - 2
= -10
Our final answer is -10
There evaluating -2x - 2(3x - 4) - x, where x is 2 = -10

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Task 3 • i. Simplify this expression: 3(2x - 1) + 2(x + 4) - 5
• ii. Evaluate this expression: (x^2 + 2x - 3) / (x + 1) when x = 2
• iii. Solve the following equation: 2x + 5 = 3(x - 2) + 1
(You are required to solve these problems at paper and these share clear photographs for adding a touch of your creativity and personal effort which should be marked with your username)

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• Task 4 A • Suppose there's a bakery selling a total of 250 loaves of bread per day. They are selling whole wheat and white bread loaves with numbers of whole wheat loaves sold being 30 more than the number of white bread loaves. If x is representing number of white bread loaves sold out and bakery is making a profit of $0.50 for each white bread loaf and $0.75 for each whole wheat loaf then please write an expression for representing bakery total daily profit.

To write an expression that represents the bakery's total daily profit, we need to break down the information.

Total loaves sold = 250
White loaves sold = x
Wheat loaves sold is 30 more than white bread loaves
Wheat loaves = x + 30

Profit per white loaves = $0.50
Profit per wheat loaves = $0.75

Profit for total white loaves = x × $0.50
Profit for total wheat loaves = x + (x +30) × $0.75

Total profit = (number of white loaves × profit per white loaves) + (number of wheat loaves × profit per wheat loaves)

The expression representing the bakery's total profit will be:

(x × $0.50) + (x + (x +30) × $0.75)

B • Suppose that cost of renting a car for a day is re-presented by the expression 2x + 15 and here x is the number of hours in which car is rented. If the rental company offers a package of 3x - 2 dollars for customers who take car at rent for more than 4 hours then write an expression for the total cost of renting the car for x hours and show how you simplify it.
(Solve the above scenario based questions and share step by step that how you reach to your final outcome)

Breaking the information down:
Daily rent = 2x + 15
Discount for 4 hours = 3x - 2

Since the company offered a discount for rent for more than 4 hours, then x is greater than 4

Therefore, total cost = Cost of rent - discount package = (2x + 15) - (3x - 2)

The expression for the total cost of renting the car for x hours is (2x + 15) - (3x - 2).

Solving for x in the expression (2x + 15) - (3x - 2)
Step 1: clear brackets
= 2x + 15 - 3x + 2
Step 2: collect like terms
= 2x - 3x + 15 + 2
= -x + 17

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Am inviting @johnmitchel, @chiomi, and @divinelife

Thanks