Basic format of algebra
Introduction :
Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Basic format of algebra is related with the four basic operations such as addition, subtraction, multiplication and division. The most important terms for basic format of algebra is variables, constant, coefficients, exponents, terms and expressions. For basic format of algebra, we have to replace the symbols and alphabets in place of unknown numbers to make a statement. Hence, basic format of algebra cause the leads of Arithmetic.
Example problems for basic format of algebra:
Example 1:
Solve the equation for x, 4(x - 6) = 28.
Solution:
4(x - 6) = 28
4 * x – 4 * 6 = 28
4x - 24 = 28 (add 24 on both sides)
4x – 24 + 24 = 28 + 24
4x = 52 (divide both sides by 4)
4x / 4 = 52 / 4
x = 26 / 2
x = 13
Example 2:
Solve the inequality for x, 3x - 3 < -x + 10.
Solution:
3x - 3 < -x + 10 (add 3 on both sides)
3x - 3+ 3 < -x + 10 + 3
3x < -x + 13 (add x on both sides)
3x + x < -x + x + 13
4x < 13 (divide both sides by 6)
4x / 4 < 13 / 4
x<3.25
Example 3:
Solve the equation for x, 3(5x + 5y) = 14. where y = 3
Solution:
3(5x + 5y) = 14. put y = 2
3(5x + 5 * 3) = 14.
3(5x + 15) = 14.
(3 * 5x) + (3 * 15) = 14
15x + 45 = 14 (add -45 on both sides)
15x + 45 – 45 = 14 – 45
15x = -31 (divide both sides by 10)
15x / 15= -31 / 15
Example 4:
Use Quadratic Formula Solver 4x2 + 24x + 20=0
Solution:
Here a = 4, b = 24 and c = 20
Discriminant: b2-4ac = 242 – 4 * 4 * 20 = 256
Discriminant (16) is greater than zero. The equation has two solutions.
x =(-b±√b2-4ac)/2a
x =(-24±√242 – 4 * 4 * 20)/2*4
or
x1,2 = (-24 ± 16) / 2 * 4
or
x1 = -8 / 8 = -1
x2 = -40 / 8 = -5
or
x1,2 = -1, -5
Example 5:
Use the factorization method for solving 4x2 + 24x + 20=0
Solution:
4x2 + 24x + 20=0
4x2 + 4x + 20x + 20=0
(4x2 + 4x) + (20x + 20) = 0
4x(x + 1) + 20(x + 1) = 0
(x + 1)(4x + 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
Problem 3:
Solve the equation for x, 5x+15=45.
The answer is x = 6
Problem 4:
Use quadratic formula for solving 5x2+30x+25=0
The answer is x 1= -1 and x2=-5
Problem 5:
Use factorizing method for solving 6x2+36x+30=0
The answer is x 1= -1 and x2=-5
I like to share this algebra problems with you all through my blog.
Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Basic format of algebra is related with the four basic operations such as addition, subtraction, multiplication and division. The most important terms for basic format of algebra is variables, constant, coefficients, exponents, terms and expressions. For basic format of algebra, we have to replace the symbols and alphabets in place of unknown numbers to make a statement. Hence, basic format of algebra cause the leads of Arithmetic.
Example problems for basic format of algebra:
Example 1:
Solve the equation for x, 4(x - 6) = 28.
Solution:
4(x - 6) = 28
4 * x – 4 * 6 = 28
4x - 24 = 28 (add 24 on both sides)
4x – 24 + 24 = 28 + 24
4x = 52 (divide both sides by 4)
4x / 4 = 52 / 4
x = 26 / 2
x = 13
Example 2:
Solve the inequality for x, 3x - 3 < -x + 10.
Solution:
3x - 3 < -x + 10 (add 3 on both sides)
3x - 3+ 3 < -x + 10 + 3
3x < -x + 13 (add x on both sides)
3x + x < -x + x + 13
4x < 13 (divide both sides by 6)
4x / 4 < 13 / 4
x<3.25
Example 3:
Solve the equation for x, 3(5x + 5y) = 14. where y = 3
Solution:
3(5x + 5y) = 14. put y = 2
3(5x + 5 * 3) = 14.
3(5x + 15) = 14.
(3 * 5x) + (3 * 15) = 14
15x + 45 = 14 (add -45 on both sides)
15x + 45 – 45 = 14 – 45
15x = -31 (divide both sides by 10)
15x / 15= -31 / 15
Example 4:
Use Quadratic Formula Solver 4x2 + 24x + 20=0
Solution:
Here a = 4, b = 24 and c = 20
Discriminant: b2-4ac = 242 – 4 * 4 * 20 = 256
Discriminant (16) is greater than zero. The equation has two solutions.
x =(-b±√b2-4ac)/2a
x =(-24±√242 – 4 * 4 * 20)/2*4
or
x1,2 = (-24 ± 16) / 2 * 4
or
x1 = -8 / 8 = -1
x2 = -40 / 8 = -5
or
x1,2 = -1, -5
Example 5:
Use the factorization method for solving 4x2 + 24x + 20=0
Solution:
4x2 + 24x + 20=0
4x2 + 4x + 20x + 20=0
(4x2 + 4x) + (20x + 20) = 0
4x(x + 1) + 20(x + 1) = 0
(x + 1)(4x + 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
Problem 3:
Solve the equation for x, 5x+15=45.
The answer is x = 6
Problem 4:
Use quadratic formula for solving 5x2+30x+25=0
The answer is x 1= -1 and x2=-5
Problem 5:
Use factorizing method for solving 6x2+36x+30=0
The answer is x 1= -1 and x2=-5
I like to share this algebra problems with you all through my blog.