Definition of algebra:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. -Source from Wikipedia.
Is this topic Gauss Elimination Method hard for you? Watch out for my coming posts.
Simple problems On Algebra:
Example 1:
Solve the algebraic expression X-3= 12
Solution:
We need to find the value of x
Step 1: X-3+3=12+3 (we need to add 3 on both the sides)
Step 2: X=15.
Example 2:
Solve the algebraic expression 3a-9=63
Solution:
We need to find the a value
Step 1: 3a-9+9=63+9 (first we need to add 9 on both the sides)
Step 2: 3a=72 (Now we divide using 3 on both the sides)
Step 3: a=24
Example 3:
Solve the algebraic expression 10+B+1=2(B+1)
Solution:
Step1 :( 11+B)=2B+2
Step 2: 11+B-B=2B-B+2 (subtract B on both the sides)
Step 3: 11=B+2
Step 4: 11-2=B+2-2 (Subtract 2 on both the sides )
Step 5: 9=B.
Example word problems:
Word Problem 1:
Marissa spent `$` 42 for shoes. This was `$` 14 less than twice what she spent for a dress. How much was the dress?
Solution:
Step 1: Let assume x be how much she spent for the dress.
Step 2: So, 2x-14=42
Step 3: 2x+14-14=42+14 (Here we need to add 14 ob both the sides)
Step 4: 2x=56(Now we divide using 2 on both the sides)
Step 5: x=56/2
Step 6: x= 28
So the dress cost is $28.
Word Problem 2:
The sum of two numbers is 84, and one of them is 12 extra than the other. What are the two numbers?
Solution:
In this problem, we need to find two numbers. So, let x be one of them. Let x be the first number.
We know that the other number is 12 more, x + 12.
Here the sum is 84:
So it can be written as x+x+12=84.
Now we need to solve this:
So, x+x+12=84.
Step 1: 2x+12 =84
Step 2: 2x-12+12=84-12 (subtract 12 on both the sides)
Step 3: 2x=72 (now we need to divide using 2 on both the sides)
Step 4: x= 36 .So the first number is 36
Now we need to find another number:
x+12 =36
So, 36+12 = 48.The another number is 48
(The sum of 36+48 is 84)
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. -Source from Wikipedia.
Is this topic Gauss Elimination Method hard for you? Watch out for my coming posts.
Simple problems On Algebra:
Example 1:
Solve the algebraic expression X-3= 12
Solution:
We need to find the value of x
Step 1: X-3+3=12+3 (we need to add 3 on both the sides)
Step 2: X=15.
Example 2:
Solve the algebraic expression 3a-9=63
Solution:
We need to find the a value
Step 1: 3a-9+9=63+9 (first we need to add 9 on both the sides)
Step 2: 3a=72 (Now we divide using 3 on both the sides)
Step 3: a=24
Example 3:
Solve the algebraic expression 10+B+1=2(B+1)
Solution:
Step1 :( 11+B)=2B+2
Step 2: 11+B-B=2B-B+2 (subtract B on both the sides)
Step 3: 11=B+2
Step 4: 11-2=B+2-2 (Subtract 2 on both the sides )
Step 5: 9=B.
Example word problems:
Word Problem 1:
Marissa spent `$` 42 for shoes. This was `$` 14 less than twice what she spent for a dress. How much was the dress?
Solution:
Step 1: Let assume x be how much she spent for the dress.
Step 2: So, 2x-14=42
Step 3: 2x+14-14=42+14 (Here we need to add 14 ob both the sides)
Step 4: 2x=56(Now we divide using 2 on both the sides)
Step 5: x=56/2
Step 6: x= 28
So the dress cost is $28.
Word Problem 2:
The sum of two numbers is 84, and one of them is 12 extra than the other. What are the two numbers?
Solution:
In this problem, we need to find two numbers. So, let x be one of them. Let x be the first number.
We know that the other number is 12 more, x + 12.
Here the sum is 84:
So it can be written as x+x+12=84.
Now we need to solve this:
So, x+x+12=84.
Step 1: 2x+12 =84
Step 2: 2x-12+12=84-12 (subtract 12 on both the sides)
Step 3: 2x=72 (now we need to divide using 2 on both the sides)
Step 4: x= 36 .So the first number is 36
Now we need to find another number:
x+12 =36
So, 36+12 = 48.The another number is 48
(The sum of 36+48 is 84)
