While Analyzing Equations and Inequalities we focus on some points. For analyzing equations and inequalities we follow some points:
1. First solve the expression.
2. Then understand and use the Properties of Real Numbers.
3. Then simplify the equation and inequalities.
4. At last find the absolute values equation and inequality.
If equal sign is present in the equations, and equation is used to find the unknown variables. One method for solving the equation is substitution method.
Suppose we have an equation p + q = 2p – 1;
We know that equation is used to find the unknown variable.
Here in this equation we solve for unknown variable ‘p’;
On solving the equation for unknown variable ‘p’ we get:
⇒ p + q = 2p – 1;
⇒p = q + 1;
Now we use substitution method:
Now substitute the value of ‘p’ in the equation:
⇒ p + q = 2p – 1;
Put p = q + 1;
⇒ (q + 1) + q = 2(q + 1) – 1;
Now we solve the value of unknown variable ‘q’.
⇒q + 1 + q = 2q + 2 – 1;
Now combine like terms:
⇒2q – 2q = 1 – 1;
This is how we solve the equation by substitution method.
And in case of inequality, if we have two variables ‘m’ and ‘n’, then there are conditions for analyzing the inequality equations.
Suppose ‘m’ is less than equal to ‘n’;
⇒ m ≤ n;
‘m’ is greater than equal to n then we can write:
⇒m ≥ n;
And if ‘m’ is greater than n then we can write;
⇒m > n;
And if ‘m’ is smaller than ‘n’ then we can write;
⇒m < n;
These all are the properties of inequality. If in any equation these symbols are present then we can say there is an inequality in the expression.
An expression is defined as the Combination of two or more terms and can be written in the form of Relations between variables and constant values. The only difference between the expression and the equation is that the sign of equal to is missing in the expression, which exists in the equation.
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When we have to solve equations, we Mean that we are finding the value of the variable, which satisfies the equations. The equations can be Linear Equations of one variable or the pair of Linear Equations with Two Variables. Firstly we are solving equations with one variable.
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By the term absolute value, we Mean that we are going to find the value of the equation, which is always a positive number. All absolute values have magnitude, but no direction and the absolute value is represented by | | sign, which we call as the modulus sign.
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The series of Real Numbers include the numbers which can be both rational and Irrational Numbers. These numbers are called real numbers as they are not imaginary. Let us look at the properties of real numbers one by one:
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Talking into consideration Solving Inequalities algebraically such as : x + 3 > 0, was a simple and easy expression and we must remember that when the expression is multiplied by any of the negative number, then the sign of inequality changes.
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Absolute value can be defined as measure of how further a number is from 0. For example: ‘10’ is 10 away from zero and -50 is 50 away from zero. Absolute value of 0 is 0 and absolute value of 5 is 5. These all are examples of Absolute Value Function. Negative Numbers are not included in absolute value function. Suppose we have any negative number then...Read More