SLC-S22W1/Variables and Expressions

Hi Friends

I am Muhammad Ahmad and I hope you all will be fine and enjoying your lives. Today I am going to participate in the First week of the Engagement Teaching Challenge which our Dear, Instructor Mr. @khursheedanwar organized. First, l would like to thank him for organizing such a great lecture. By the way in this Lecture, we are gonna learn about Algebra what is Algebra? So without wasting any time let's get into it.

To understand this, first of all, we have to know about, What Is variables and expressions.

Variable:

The variable is a symbol that is usually used in expressions. It is usually a letter like x or y etc. The variable is changeable in some equations we can suppose x with 2 and in some equations we can suppose the same x with 3.Basically Variable is a symbol that is used to represent an unknown value.

Expression:

Expression is a combo of Constant numbers, Variables, and some other mathematical operations like plus+, minus-, multiplication and division, etc.

Qualitative Variable:

The type of Variable in which it can't be described by numbers.Like the hair of a tiger. As we know counting the hair of a Tiger is impossible thus it means that this is Qualitative Variable.

Quantitative Variable:

The type of Variable can be described by numbers. Like how many tigers are there with black hairs? In this, we can count tigers which simply means that it is a Quantitative Variable.

Monomial Expression:

In this type of expression, there is only one type. We can better understand this with a proper example like ( 5x ) here in this example there is only one term which means this is Ma onomial Expression.

Binomial Expression:

This type of expression has only 2 terms. An example of a binomial is ( 2x+3) here in this expression there are two terms which are separated by a mathematical operation of + which simply means that it is a Binomial Expression.

For this, we have to solve an expression. I have got an expression, and I have taken an expression.

Expression is:

Let's solve this expression step by step.

= 2x+7y-92

• Suppose x=9 and y=2.

Now put the values of x and y in the given expression. We got:

= 2(9)+7(2)-92

According to the PEMDAS rule, we have to multiply 2 by 9 then multiply 7 by 2, and then write it as the same.

= 18+14-92

Now again using PEMDAS and that time we have to Add 18 with 14 then we get: 32..
Now we have to subtract 32 from 92. We get: 60

Like we have:
= 18+14-92
= 32-92
= 60

The required answer is 60

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

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

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

Scenario: 1

• Let x represent the white bread loves per day.
• As we know the number of loaves is 30 so the number of wheat loves is x+30 → Equation 1

As we know the bakery is selling 250 bread loves daly. So we can write Equation 1 as:

x+(x+30) = 250
Now simplifying this.
2x+30 = 250
2x = 250−30
2x = 220
Dividing 2 on both sides.
x = 110
So,

The white bread loves is equal to x and x is now equal to 110.

Now we have to write the Expression for the profit.
As we know from the question the bakery is earning $0.50 for 1 white bread loaf and $0.75 for each wheat bread loaf.

Now to find the Profit we have to put the exact amount of the loafes in this:

• Profit= ( Profit of the White Bread loaf × No of White Bread loaves)+(Profit per whole Wheat loaf × No of whole Wheat loaves)

Putting values then we get:
Profit = 0.50x+0.75 (x+30)
Profit=0.50x+0.75x+22.5
Now combing the like terms : (0.50x+0.75x)
Now we get:
Profit = 1.25x+22.5

As we find the value of x at first which was equal to 110. Now putting that value here as doing substituting.Then we get:

Profit = 1.25(110)+22.5
Profit=137.5+22.5
Profit=160

The bakery's daily profit is: 160 Dollars or $160

Scenario: 2

• Let x be the hour for renting a car. As in the expression 2x+15, (x is the number of hours)
• Customer Renting a car for more than 4 hours. The given Expression for this is: 3x−2

Now we have to write the Expression for the total cost.

The total cost combined with the normal cost of rent hourly is: (2x+15) and the package mentioned is (3x-2).

So,

Total Cost = (2x+15) + (3x−2)

Simplifying the Expression of the Total Cost.

Expression is (2x+15) + (3x−2)
Combining the Like Terms

• For Variables: 2x+3x = 5x
• For Constants: 15−2 = 13

Total Cost = 5x+13

So the total cost of renting a car when there is pa ackage is 5x+13.

• I would like to invite Dear. @chant, Dear. @sahar78, and Dear. Mam @suboohi to participate in this. Once again Thank you so much. I am highly obliged.