Inequality Equations In this article we are going to discuss about concept called algebra equations and inequalities. Equation: Two expressions are in equal is called an equation. For example: x + 3 = 2, x + 2 = 1,…. When we add, subtract, multiply or divide the same number on both the side of the equation, the equal sign of an equation does not change. Inequality: Two algebraic expressions or two real numbers related by the symbol ‘<’, ‘>’, ‘<=’ or ‘>=’ form an inequality. Added or subtracted by the same number on both side of the inequality. Multiplied or divided by the same number on both side of the inequality but if we divide or multiply by a negative number, we must reverse the inequality sign. Know More About Simplifying Radicals Calculator
How to Solve Equations Below are the examples based on how to solve equations Example 1: Solve the equation for the variable y: y - 20 = 30 Solution: y - 20 = 30 Add 20 on both sides of the equation y - 20 + 20 = 30 + 20 y = 50 So, the answer is y = 50. Example 2: Solve the equation for the variable x: ( ) + 40 = 30 Solution: Learn More About Rational Expressions Calculator
() + 40 = 30 Subtract 40 on both sides of the equation () + 40 - 40 = 30 - 40 () = -10 Multiply 3 on both sides of the equation () * 3 = -10 * 3 y = -30 So, the answer is 30.
Now taking out the common terms gives x(x + 3) - 2(x + 3) = 0 This finally yields (x + 3)(x - 2) = 0 Here x = -3, 2 are the factors of the given equation. How to Solve Inequalities Below are the examples on how to solve inequalities Example 1 : Solve the inequality: 8x + 5 < 6x +7. Solution : We have, 8x + 5 < 6x +7 Subtract 6x on both sides of the equation 8x - 6x + 5 < 6x + 7 - 6x 2x + 5 < 7 Subtract 5 on both sides of the equation
Binary Operations Binary opeation is the one of the operations which is used in the mathematics. A binary operation on A is a rule that we have to assigns to every pair of elements of A a unique element of A. We are using the addition and multiplication of real numbers these are the examples of binary operations. (1) '+' is a binary operation on the set of naturals. (2) '.' is a binary operation on the set of naturals. ∴ ( i ) ∀ a, b ∈ N, a + b ∈ N. ( ii ) ∀ a, b ∈ N, a.b ∈ N. ( iii ) ' - ' is not a binary operation on N. ∴ 1 - 1 = 0, but 0 ∉ N. ( iv ) Addition, subtraction and multiplication are binary operations on I.
Binary Operations are as given below, Commutative Law Associative Law Relationship between Commutative and Associative Binary OperationBack to Top Below you could see relationship between commutative and associative binary operation Commutative law Let * be a binary operation on the set S. * is said to be commutative in S if a, b Îľ S, a * b = b * a Associative Law Let * be a binary operation on the set S. * is said to be an associative in S if a, b Îľ S, a * (b * c) = (a * b) * c. Points to remember about binary operations 1. '+' & '.' are commutative and associative in the sets, N, I, Q, Q', R and C. Read More About Partial Derivative Calculator
i.e, a + b = b + a and a.b = b.a a + (b + c) = (a + b) + c 2. ' - ' and ' รท ' are neither commutative nor associative. Classification of Binary OperationsBack to Top Below you could see classification of binary operations for addition, subtraction and multiplication Addition: The Binary addition is the simple and easy to work that and that operations are simple of the binary operations, so we can see that to add two binary numbers and mainly three things is there you can remember that while adding the binary numbers. For example, 0 + 0 is 0 carry 0 (its easy) 0 + 1 is 1 carry 0 1 + 1 is 0 carry 1. Subtraction: The subtraction is the simplest one it is relevant to the addition one just same
as the normal subtraction with the borrowing and subtracting. Now we try 1101 (13 in base 10) minus 110 (6 in base 10): 1101 - 110 -------From the right to the left we need to start that,first one is 1 is there so we can start with the one 1 minus 0 the answer will be 1. Next 0 minus 1 is impossible to subtract from the 0.so you can from the next digit borrow from next number to left, make the as greater as top number 10(10)1, then 10 minus 1 is 1 the answer is 1. Next 0 minus 1 is not possible again same as the previous one, so we can go through the same thing, by making the number as 0(10)01 and 10 minus 1 is again 1 then the final result is 7 or 111 in base 10, which is correct. Multiplication: The Binary multiplication is the simple same as the normal multiplication in the form, so we can see that binary multiplication also easy. Multiply the two binary numbers..
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