"SLC-S22W1/Variables and Expressions"

sheikhtuhin (60)in #algebra-s22w1 • 2 days ago

In the name of Allah, the Most Gracious, the Most Merciful.

Dear friends, today I am going to join "SLC S22W1//Variables and Expressions" this learning challenge is organized by @khursheedanwar sir.I am very grateful to Sir for finding such a beautiful learning challenge topic and teaching us there.Right now I'm trying to highlight my learnings here.

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

Variable:

If I may say, in algebra a variable is something that represents an unknown quantity.And there, if I have two operators in an equation using any value, I can find the value of any unknown quantity to determine one of the values.In a word, it is something that represents the unknown number in an equation.

For example, ( 3p+q=0) This equation has two unknowns that we can treat as variables, P and Q.

However, the value of a variable can be positive, negative, or any combination of these; it cannot have a specific value.

Expression:

An expression is a string of numbers in an equation that, when combined, produces a specific result.In this case, if multiple quantities are combined using a plus or minus sign on the left side of the equation, all of them are considered together as an expression.

For example, If an equation is (P+Q+R=0), then the entire number on the opposite side of zero will be considered an expression. In my limited knowledge, this is all I can analyze and that is what I understand.

Task-2•Show your way of evaluating of an algebraic expression if values of variables are given? Step by step explanation required!

Where the zodiac signs are given, there may be several ways to solve it.In this case, to simplify, you have to pay attention to brackets, indices, symbols, etc.
For example, in the case of parentheses, the first parentheses work.Then the work inside the second bracket, then the work inside the third bracket, and finally, if there is anything outside, its work.
Again, if there is division and multiplication in the case of symbols, then the division must be done first, followed by the multiplication.Finally, I have to solve a problem using addition and subtraction.But I'm not saying that if the value of the variable is given, then solving it becomes very easy.

If a variable is "x" then its value is given as 5.

In the case of the equation (x+5) is given.
In this case, I will directly set the value of x.Then (5+5=10)The value will come out directly.

In this case, the teacher taught BODMAS to solve simple arithmetic problems in seventh grade.Accordingly, we would have solved what I have already briefly mentioned above.

Task-3• (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)

I am providing step-by-step pictures of all these tasks, along with the answers I wrote in my notebook.

Simplify this expression: 3(2x - 1) + 2(x + 4) - 5

Simplified:
3(2x-1)+2(x+4)-5
= 6x-3+2x+8-5
=8x+8-8
= 8x

Evaluate this expression: (x^2 + 2x - 3) / (x + 1) when x = 2

(X^2+2x-3)/X+1
= (2^2+2*2-3)/(2+1)
=(4+4-3)/3
= 5/3

Solve the following equation: 2x + 5 = 3(x - 2) + 1

Ans:

 2x+5=3((x-2)+1

=> 2x+5 = 3x-6+1
=> 2x-3x= -6-5+1
=> -x= -10
=> X= 10 [Multiply both sides by -1]

Task-4•Solve the above scenerio based questions and share step by step that how you reach to your final outcome

I am presenting my writings here, including the final stages of work I wrote in a notebook.

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.

Given,
Total number of loaves sold = 250
And the number of white bread = X
Whole wheat =(X+30)

According to the conditions,

 X+(x+30)= 250

=> 2x+30=250
=> 2x=250-30
=> 2x=220
=> X=220/2
=X=110

Since x=number of white bread.
Then the number of white breads is 110.

Whole wheat =(X+30)
=(110+30)
=140

Given price of a white bread = $0.50
Price of 110 white breads = ($0.50*110)
= 55$

Again, the price of a whole wheat loaf = $0.75
Price of 140 whole wheat loaves = ($0.75*140)
= 105$

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.

Car rental price in less than four hours = (2x+15)
Where, X is the number of hours to rent the car.

Again,
Offer by the company for car rental in less than four hours = (3x-2)

If, x≤4, cost = (2x+15)
If, x>, cost= (3x-2)

Since both the expressions given here are simple, there is no scope for simplification, but it can be expressed as an expression. The expression and simplification are given below.

F(x)= {2x+15,€ x≤4}
F(x)={3x-2 €x>4}

I tried to present this as a function that I studied from the chapter on set functions.I can't say with 100% certainty whether this is actually correct or not, but I had to take this little help from the textbook.