Algebra basic formats
Introduction :
Algebra is one of the important branch of mathematics. Algebra plays an important role in day life. Basic format of algebra has four basic operations such as addition, subtraction, division and multiplication.The most important terms of algebra are variables, coefficients, exponents and expressions. In basic format of algebra, we can replace the symbols and alphabets in the place of unknown numbers in a statement. Let us see some example problems, whch will help to understand the concept clearly.
Example Problems for Algebra basic formats:
Example 1:
Solve the following equation for x, 6(x -4) = 20
Solution:
6(x - 4) = 20
6* x – 6 * 4 = 20
6x – 24 = 20 (add 24 on both sides)
6x – 24 + 24 = 20 + 24
4x = 44 (divide both sides by 4)
`4x / 4 = 44 / 4`
`x = 22/ 2`
x = 11
Example 2:
Solve the inequality for x, 4x - 3 < -x + 5.
Solution:
4x - 3 < -x + 3 (add 3 on both sides)
4x - 3+ 3 < -x + 5 + 3
4x < -x + 8(add x on both sides)
4x + x < -x + x + 8
5x < 8
x<1.6
Solve the equation for x, 2(4x + 5y) = 10. where y = 2
Solution:
2(4x + 5y) = 10. put y = 2
2(4x + 5 * 2) = 10.
2(4x + 10) = 10.
(2 * 4x) + (2 * 10) = 10
8x + 20 = 10(add -20 on both sides)
8x + 20 – 20 = 10 – 20
8x = -10 (divide both sides by 10)
X=-1.25
Example 4:
Use quadratic formula for solving the given equation 2x2 + 10x + 20=0
Solution:
a = 4, b = 10 and c = 20
Discriminant:` b^2-4ac` = 102 – 4 * 4 * 20 = 220
Discriminant (16) is greater zero. The equation has two solutions.
`x =((-b+-sqrt(b^2-4ac))/(2a))`
x =`(-10+-sqrt(10^2-4*4*20))/(2*4)`
or
`x1,2 = (-20+-16)/(2 * 4)`
or
`x1 = -8 = -1`
`x2 = -40 / 8 = -5`
or
x1,2 = -1, -5
Example 5:
Solve the factorization method for the following equation 2x2 + 22x + 20=0
Solution:
2x2 + 24x + 20=0
2x2 + 2x + 20x + 20=0
(2x2 +2 x) + (20x + 20) = 0
2x(x + 1) + 20(x + 1) = 0
(x + 1)(2x + 20) = 0
X + 1=0 and 4x + 20 = 0
X + 1 – 1 = 0 - 1 and 4x + 20 – 20 = 0 - 20
x=-1 and x=-5
Therefore, x=-1, -5
Practice Problems for Basic Format of Algebra:
Problem 1:
Solve the equation for x, 2x-13=-8.
The answer is x = 2.5
Problem 2:
Solve the inequality for x, 3x-34=56
The answer is x = 30
Algebra is one of the important branch of mathematics. Algebra plays an important role in day life. Basic format of algebra has four basic operations such as addition, subtraction, division and multiplication.The most important terms of algebra are variables, coefficients, exponents and expressions. In basic format of algebra, we can replace the symbols and alphabets in the place of unknown numbers in a statement. Let us see some example problems, whch will help to understand the concept clearly.
Example Problems for Algebra basic formats:
Example 1:
Solve the following equation for x, 6(x -4) = 20
Solution:
6(x - 4) = 20
6* x – 6 * 4 = 20
6x – 24 = 20 (add 24 on both sides)
6x – 24 + 24 = 20 + 24
4x = 44 (divide both sides by 4)
`4x / 4 = 44 / 4`
`x = 22/ 2`
x = 11
Example 2:
Solve the inequality for x, 4x - 3 < -x + 5.
Solution:
4x - 3 < -x + 3 (add 3 on both sides)
4x - 3+ 3 < -x + 5 + 3
4x < -x + 8(add x on both sides)
4x + x < -x + x + 8
5x < 8
x<1.6
Solve the equation for x, 2(4x + 5y) = 10. where y = 2
Solution:
2(4x + 5y) = 10. put y = 2
2(4x + 5 * 2) = 10.
2(4x + 10) = 10.
(2 * 4x) + (2 * 10) = 10
8x + 20 = 10(add -20 on both sides)
8x + 20 – 20 = 10 – 20
8x = -10 (divide both sides by 10)
X=-1.25
Example 4:
Use quadratic formula for solving the given equation 2x2 + 10x + 20=0
Solution:
a = 4, b = 10 and c = 20
Discriminant:` b^2-4ac` = 102 – 4 * 4 * 20 = 220
Discriminant (16) is greater zero. The equation has two solutions.
`x =((-b+-sqrt(b^2-4ac))/(2a))`
x =`(-10+-sqrt(10^2-4*4*20))/(2*4)`
or
`x1,2 = (-20+-16)/(2 * 4)`
or
`x1 = -8 = -1`
`x2 = -40 / 8 = -5`
or
x1,2 = -1, -5
Example 5:
Solve the factorization method for the following equation 2x2 + 22x + 20=0
Solution:
2x2 + 24x + 20=0
2x2 + 2x + 20x + 20=0
(2x2 +2 x) + (20x + 20) = 0
2x(x + 1) + 20(x + 1) = 0
(x + 1)(2x + 20) = 0
X + 1=0 and 4x + 20 = 0
X + 1 – 1 = 0 - 1 and 4x + 20 – 20 = 0 - 20
x=-1 and x=-5
Therefore, x=-1, -5
Practice Problems for Basic Format of Algebra:
Problem 1:
Solve the equation for x, 2x-13=-8.
The answer is x = 2.5
Problem 2:
Solve the inequality for x, 3x-34=56
The answer is x = 30