SLC-S22W2/Equations and inequalities
Hello friends, how are you all doing today, hope that you people will be fine and doing great in life. @khursheedanwar organized a contest about mathematics field.
"Mathematics"
TASK 1
| Linear Equations and Inequalities |
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- Equations and Inequalities are found in Algebra; algebra is the field of mathematics which deals with linear and quadratic equations.
- Equations are just like two clauses which on combining make a sentence, so equations are 2 expressions on both side of the equality(=), both of the expressions are equal to each other.
Examples: x + y = 10, the value of x and y is different from each other but when they are added with each other it will be equal to 10. For example, the value of X is 3 and Y is 7 which on addition equal to 10. Moreover, x-y=5; this means that value of x is larger than y and on solving the equation it will be equal to 5.
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- Now, Inequality are 2 expressions, one of the equation can be greater from the other one or it can be greater and equal to that expression.
Examples: x + 5 > 8, this means that the expression on left side is greater than the right one. The value of x must be greater than 3 which will prove the sentence right.
Task 2
| Different Types Of Inequalities |
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- The different types of inequalities can contain 3 expressions and greater or equal sign to prove the equations.
For Example;
In the first example I have used an inequality, a single inequality and explained it.
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In this second example, I have used 2 inequalities and explained them in the photo.
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Task 3
| Solve |
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- 2x + 5 = 11, this a linear equation. I am going to find the answer of x by solving this equation.
=> 2x = 11 - 5
=> x = 6 / 2
=> x = 3
Task 4
| Equation | If Tom wants for making x cakes and he has 10 cups of flour, 8 cups of sugar and 4 cups of cocoa powder then calculate number of cakes that can be made by Tom? |
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Given:
1 Chocolate cake recipe needs 2 cups of flour, 1 cup of sugar and 1/2 cup of cocoa powder. (2 cups flour, 1 cup sugar and 1/2 cup of cocoa).
let x = cakes, y = flour cups, z = cups of sugar and w = cups of cocoa.
Equation => x = y + z + w.
1x = 2y + z + 1/2w
Question: find x,
10y, 8z and 4w.
Answer: 2 cups of flour are used to make 1 cake, so 10 cups will make 5 cakes. 1 cup sugar can be used in 1 cake so 8 cups for 8 cakes and half cup of cocoa is used in 1 cake so 4 cups will be used in 8 cakes.
Due to limitation of flour we can only make 5 cakes because the other two things are present in more quantity, as they can be used to make 8 cakes.
Thus, the possibility is to make only 5 cakes.
Equation for 5 cakes => 5x =10y + 5z + 2w
| Inequality | Tom wants for making sure that he has sufficient sugar for meeting needs for his chocolate cake. He also knows that each cake needs 1 cup of sugar and he has 8 cups of sugar which are available. He also knows that he wants to make at least 6 cakes |
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Answer: Tom has 8 cups of sugar and he needs at least 6 cakes to be prepared.
This means that x will be greater than or equal to 6 and he cannot make more than 8 cakes.
=> x ≥ 6, at least 6 cakes. (The question says that minimum 6 cakes should be prepared).
=> limitation, 8 sugar cups are available so we can make at most 8 cakes, so; x ≤ 8
=> Thus, 6 ≤ x ≤ 8
- Ashley car can hold 12 gallons; maximum quantity of 12 gallons.
- City A to city B is 240 miles.
- 1 gallon can cover 20 miles.
- Ashley have 2 gallons and wants to store 1 gallon after reaching city B.
- Find the gallons he needs to fill?
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| Inequality | x + 2 ≥ (240/20) - 1 |
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=> x + 2 ≥ (240/20) - 1
=> x ≥ 12 - 1 - 2
=> x ≥ 9
- Ashley needs to purchase 9 or more than 9 gallons of gas
Inviting my friends @paholags @sana-khan01 @nsijoro
¡Holaaa amigo!🤗
Te cuento que las ecuaciones, literalmente me hicieron llorar en el colegio jajajajaja y es que, definitivamente las matemáticas y yo no fuimos y tampoco seremos buenas amigas. Pero me alegra mucho saber que tú tienes una buena relación con ellas.
Te deseo mucho éxito en la dinámica... Un fuerte abrazo💚