Introduction to basic algebra:
Basic 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. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. The part of algebra called elementary or basic algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers, such as addition.In this article we shall discuss about basics of algebra (Source:Wikipedia)
Please express your views of this topic Compound Inequalities Word Problems by commenting on blog.
Sample problem for basic algebra:
Example 1:
Solve the algebra equation.
|2x – 1| = 7
Solution:
Step 1: The absolute value of the given equation is already inaccessible.
Either 2 x-1 = +7 or 2 x - 1= -7
Step 2: Solve the equation 2 x – 1 =+7
2 x – 1 = 7
2 x = 8
X = 4
Step 3: Solve the equation 2x-1=-7
2 x – 1 = -7
2 x = -6
X = -3
The answers are 4 and -3. The answers may not be solutions to the equation.
Check the answer x=4 by replacement 4 in the given equation for x. If the left side of the equation sum value is equals the right side of the equation sum value after the replacement of x value, you have got the exact answer.
Left side: |2 (4) – 1 | = 7
Right Side: 7
Check the answer x = -3 by replacement -3 in the given equation for x. If the left side of the equation sum value is equals the right side of the equation sum value after the replacement of x value, you have got the exact answer.
Left Side: | 2 ( -3) – 1 | = - 7
Right Side: -7
The answer of the equation are x=4 and -3.
Example 2:
Solve the equation
`sqrt(x - 7)` = 4
Solution:
The reality of that you cannot get the square root of a negative number. Therefore the values of x - 7 or x +7 .
we take Square on both sides of the equation.
( `sqrt(x - 7)` )2 = (4)2
X - 7 = 16
Add 7 to both sides of the equation.
x - 7 +7 = 16 + 7
x = 23
The answer is x=23.
Solve the given practice problem
7(-3x - 4) - (-7x - 6) = -2(7x + 3) -16
Solution:
Simplifying the given expression.
-21x - 28 + 7x +6 = -14x - 6 -16
We should Grouping the terms like below.
-14x - 22 = -14x - 22
Add 14x + 22 to both sides and write the equation as follows
0 = 0
The above declaration is right for all values of x and then all actual numbers are answer to the given equation.
I have recently faced lot of problem while learning Solving Linear Equations and Inequalities, But thank to online resources of math which helped me to learn myself easily on net.
Practice problem:
Solve |2x – 1| = 9
Ans: x = 5, -4
Solve |2x – 1| = 11
Ans: x = 6, -5
Solve the given practice problem |3x – 3| = 12
Answer: X = -3
Solve 13− (5x + 9) = -3x
Answer: x = 2
Basic 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. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. The part of algebra called elementary or basic algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers, such as addition.In this article we shall discuss about basics of algebra (Source:Wikipedia)
Please express your views of this topic Compound Inequalities Word Problems by commenting on blog.
Sample problem for basic algebra:
Example 1:
Solve the algebra equation.
|2x – 1| = 7
Solution:
Step 1: The absolute value of the given equation is already inaccessible.
Either 2 x-1 = +7 or 2 x - 1= -7
Step 2: Solve the equation 2 x – 1 =+7
2 x – 1 = 7
2 x = 8
X = 4
Step 3: Solve the equation 2x-1=-7
2 x – 1 = -7
2 x = -6
X = -3
The answers are 4 and -3. The answers may not be solutions to the equation.
Check the answer x=4 by replacement 4 in the given equation for x. If the left side of the equation sum value is equals the right side of the equation sum value after the replacement of x value, you have got the exact answer.
Left side: |2 (4) – 1 | = 7
Right Side: 7
Check the answer x = -3 by replacement -3 in the given equation for x. If the left side of the equation sum value is equals the right side of the equation sum value after the replacement of x value, you have got the exact answer.
Left Side: | 2 ( -3) – 1 | = - 7
Right Side: -7
The answer of the equation are x=4 and -3.
Example 2:
Solve the equation
`sqrt(x - 7)` = 4
Solution:
The reality of that you cannot get the square root of a negative number. Therefore the values of x - 7 or x +7 .
we take Square on both sides of the equation.
( `sqrt(x - 7)` )2 = (4)2
X - 7 = 16
Add 7 to both sides of the equation.
x - 7 +7 = 16 + 7
x = 23
The answer is x=23.
Solve the given practice problem
7(-3x - 4) - (-7x - 6) = -2(7x + 3) -16
Solution:
Simplifying the given expression.
-21x - 28 + 7x +6 = -14x - 6 -16
We should Grouping the terms like below.
-14x - 22 = -14x - 22
Add 14x + 22 to both sides and write the equation as follows
0 = 0
The above declaration is right for all values of x and then all actual numbers are answer to the given equation.
I have recently faced lot of problem while learning Solving Linear Equations and Inequalities, But thank to online resources of math which helped me to learn myself easily on net.
Practice problem:
Solve |2x – 1| = 9
Ans: x = 5, -4
Solve |2x – 1| = 11
Ans: x = 6, -5
Solve the given practice problem |3x – 3| = 12
Answer: X = -3
Solve 13− (5x + 9) = -3x
Answer: x = 2
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