Algebra institute
Introduction:
Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra institute cover the four basic operations in algebra such as addition, subtraction, multiplication and division. The most important terms of algebra, variables, constant, coefficients, exponents, terms and expressions are explained in algebra institute. we will know the symbols and alphabets in the place unknown values by algebra institute.
Example problems to algebra institute:
Example 1:
Solve the equation for x, 34x + 37 = 48
Solution:
34x + 37 = 48 add -37 on both sides
34x + 37 – 37 = 48– 37
34x = 3 divide both terms by 34
`(34x)/34` = `11/34`
x = .32
Example 2:
Add the following expression. (5x + 5) - (7x + 5)
Solution:
(5x + 5) - (7x + 5) Now we have to multiply “–“ with the expression 7x + 5. So we get,
= 5x + 5- 7x + 5 now we have to group the terms. So we get,
= 5x – 7x + 5 – 5
= -2x
Example 3:
Solve the equation for x, `(3x-35)/4 ` = 37 .
Solution:
`(3x-35)/4` = 37 (multiply both sides by 4)
`(3x-35)/4` `xx` 4= 37 × 4
3x – 35= 148 (add both sides by 35)
3x – 35+ 35= 148 + 35
3x = 183 (divide both sides by 3)
`(3x)/3 ` = `183/3`
x = 61
Example 4:
Find the intercepts for the following equation 2x + 4y = 5
Solution:
2x + 4y = 5
X – Intercept:
For finding x intercept, we have to plug-in y=0.
2x + 4(0) = 5
2x = 5 now we have to divide both sides by 2.
`(2x)/2` = `5/2`
X = 2.5
Y- intercept:
For finding y intercepts , we have to plug-in x=0.
2(0) + 4y = 5
4y = 5 now we have to divide both sides by 4.
`(4y)/4` = `5/4`
Y= 1.25
Example 5:
Multiply the following terms (4`x^5` ) ( 5`x^5` `y^3` ).
Solution:
(4`x^5)` ( 5`x^5` `y^3` ) we have to multiply 4x^3 with 8x^5y^3like below.
= 4`x^5` × 5`x^5` `y^3`
= 20 `x^5` × `x^5` `y^3` Note: (a`^m` ) (a`^ n` ) = a`^(m + n)`
= 20 `x^10` `y^3`
Practice problems to algebra institute:
Problem 1:
Solve the equation for x, 4x + 39 = 39.
The answer is x = 0
Problem 2:
Multiply the following terms (5x) ( 4x + 3).
Solution is 20x^2 + 15x
Problem 3:
Solve the equation for x, 3x - 33 = 36
The answer is x = 1
Problem 4:
Find the intercepts for the following equation 5x + 5y = 5
Solution is: x – intercept = 1; y – intercept = 1
Problem 5:
Multiply the following terms (5`x^6` `y^3` ) ( 4`x^3` `y^3` ).
Solution is 20 `x^9``y^6`
Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra institute cover the four basic operations in algebra such as addition, subtraction, multiplication and division. The most important terms of algebra, variables, constant, coefficients, exponents, terms and expressions are explained in algebra institute. we will know the symbols and alphabets in the place unknown values by algebra institute.
Example problems to algebra institute:
Example 1:
Solve the equation for x, 34x + 37 = 48
Solution:
34x + 37 = 48 add -37 on both sides
34x + 37 – 37 = 48– 37
34x = 3 divide both terms by 34
`(34x)/34` = `11/34`
x = .32
Example 2:
Add the following expression. (5x + 5) - (7x + 5)
Solution:
(5x + 5) - (7x + 5) Now we have to multiply “–“ with the expression 7x + 5. So we get,
= 5x + 5- 7x + 5 now we have to group the terms. So we get,
= 5x – 7x + 5 – 5
= -2x
Example 3:
Solve the equation for x, `(3x-35)/4 ` = 37 .
Solution:
`(3x-35)/4` = 37 (multiply both sides by 4)
`(3x-35)/4` `xx` 4= 37 × 4
3x – 35= 148 (add both sides by 35)
3x – 35+ 35= 148 + 35
3x = 183 (divide both sides by 3)
`(3x)/3 ` = `183/3`
x = 61
Example 4:
Find the intercepts for the following equation 2x + 4y = 5
Solution:
2x + 4y = 5
X – Intercept:
For finding x intercept, we have to plug-in y=0.
2x + 4(0) = 5
2x = 5 now we have to divide both sides by 2.
`(2x)/2` = `5/2`
X = 2.5
Y- intercept:
For finding y intercepts , we have to plug-in x=0.
2(0) + 4y = 5
4y = 5 now we have to divide both sides by 4.
`(4y)/4` = `5/4`
Y= 1.25
Example 5:
Multiply the following terms (4`x^5` ) ( 5`x^5` `y^3` ).
Solution:
(4`x^5)` ( 5`x^5` `y^3` ) we have to multiply 4x^3 with 8x^5y^3like below.
= 4`x^5` × 5`x^5` `y^3`
= 20 `x^5` × `x^5` `y^3` Note: (a`^m` ) (a`^ n` ) = a`^(m + n)`
= 20 `x^10` `y^3`
Practice problems to algebra institute:
Problem 1:
Solve the equation for x, 4x + 39 = 39.
The answer is x = 0
Problem 2:
Multiply the following terms (5x) ( 4x + 3).
Solution is 20x^2 + 15x
Problem 3:
Solve the equation for x, 3x - 33 = 36
The answer is x = 1
Problem 4:
Find the intercepts for the following equation 5x + 5y = 5
Solution is: x – intercept = 1; y – intercept = 1
Problem 5:
Multiply the following terms (5`x^6` `y^3` ) ( 4`x^3` `y^3` ).
Solution is 20 `x^9``y^6`