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Algebra Básic
Algebra
Algebra is the branch of mathematics that helps in the representation of problems or
situations in the form of mathematical expressions. It involves variables like x, y, z, and
mathematical operations like addition, subtraction, multiplication, and division to form a
meaningful mathematical expression. All the branches of mathematics such as trigonometry,
calculus, coordinate geometry, involve the use of algebra. One simple example of an
expression in algebra is 2x + 4 = 8.
Algebra deals with symbols and these symbols are related to each other with the help of
operators. It is not just a mathematical concept, but a skill that all of us use in our daily life
without even realizing it. Understanding algebra as a concept is more important than solving
equations and finding the right answer, as it is useful in all the other topics of mathematics
that you are going to learn in the future or you have already learned in past.
What is Algebra?
Algebra is a branch of mathematics that deals with symbols and the arithmetic operations
across these symbols. These symbols do not have any fixed values and are called variables. In
our real-life problems, we often see certain values that keep on changing. But there is a
constant need to represent these changing values. Here in algebra, these values are often
represented with symbols such as x, y, z, p, or q, and these symbols are called variables.
Further, these symbols are manipulated through various arithmetic operations of addition,
subtraction, multiplication, and division, with an objective to find the values.
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Solutions to Algebra Problems
algebra problems are presented.
Solution to Problem 1:
Given the equation
5 (- 3 x - 2) - (x - 3) = - 4 (4 x + 5) + 13
Multiply factors.
-15 x - 10 - x + 3 = - 16 x - 20 + 13
Group like terms.
- 16 x - 7 = - 16 x - 7
Add 16x + 7 to both sides and write the equation as follows
0 = 0
The above statement is true for all values of x and therefore all real numbers are solutions to
the given equation.
Solution to Problem 2:Given the algebraic expression
2 (a -3) + 4 b - 2 (a - b - 3) + 5
Multiply factors.
= 2 a - 6 + 4 b - 2 a + 2 b + 6 + 5
Group like terms.
= 6 b + 5
Problem 3:Given the expression
| x - 2 | - 4 | -6 |
If x < 2 then x - 2 < 0 and if x - 2 < 0 then |x - 2| = - (x - 2).
Substitute |x - 2| by - (x - 2) and | - 6 | by 6
|x - 2| - 4| -6 | = - (x - 2) - 4(6) = - x - 22
4:The distance d between points (-4 , -5) and (-1 , -1) is given by
d = √[ (-1 - (-4)) 2 + (-1 - (-5)) 2 ]
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Simplify.
d = √(9 + 16) = 5

### Unformatted Attachment Preview

Algebra – Básic Algebra Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression. All the branches of mathematics such as trigonometry, calculus, coordinate geometry, involve the use of algebra. One simple example of an expression in algebra is 2x + 4 = 8. Algebra deals with symbols and these symbols are related to each other with the help of operators. It is not just a mathematical concept, but a skill that all of us use in our daily life without even realizing it. Understanding algebra as a concept is more important than solving equations and finding the right answer, as it is useful in all the other topics of mathematics that you are going to learn in the future or you have already learned in past. What is Algebra? Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division, with an objective to find the values. Solutions to Algebra Problems algebra problems are presented. Solution to Problem 1: Given the equation 5 (- 3 x - 2) - (x - 3) = - 4 (4 x + 5) + 13 Multiply factors. -15 x - 10 - x + 3 = - 16 x - 20 + 13 Group like terms. - 16 x - 7 = - 16 x - 7 Add 16x + 7 to both sides and write the equation as follows 0=0 The above statement is true for all values of x and therefore all real numbers are solutions to the given equation. Solution to Problem 2:Given the algebraic expression 2 (a -3) + 4 b - 2 (a - b - 3) + 5 Multiply factors. =2a-6+4b-2a+2b+6+5 Group like terms. =6b+5 Problem 3:Given the expression | x - 2 | - 4 | -6 | If x < 2 then x - 2 < 0 and if x - 2 < 0 then |x - 2| = - (x - 2). Substitute |x - 2| by - (x - 2) and | - 6 | by 6 |x - 2| - 4| -6 | = - (x - 2) - 4(6) = - x - 22 4:The distance d between points (-4 , -5) and (-1 , -1) is given by d = √[ (-1 - (-4)) 2 + (-1 - (-5)) 2 ] Simplify. d = √(9 + 16) = 5 Name: Description: ...
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