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It is important to know several techniques for solving equations and inequalities because one may work better than another in a particular situation.

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Q: Why is it important to know various techniques for solving systems of equations and inequalities?

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One important difference between solving equations and solving inequalities is that when you multiply or divide by a negative number, then the direction of the inequality must be reversed, i.e. "less than" becomes "greater than", and "less than or equal to" becomes "greater than or equal to".Actually, from a purist's sense, the reversal rule also applies with equations. Its just that the reversal of "equals" is still "equals". The same goes for "not equal to".

it often simplifies arithmetic

Just keep doing the same thing to both sides of the equation at every step.

Mainly, in the case of simple inequalities, you have to remember that when multiplying or dividing by a negative number, the direction of the inequality changes, for example, from greater-than to less-than or vice versa. Also, for more complicated inequalities, such as those that involve polynomials or absolute values, additional steps are required.

To make them look more familiar and approachable to beginning algebra students. It's completely unnecessary with the advent of calculators though.

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Solving inequalities and equations are the same because both have variables in the equation.

One important difference between solving equations and solving inequalities is that when you multiply or divide by a negative number, then the direction of the inequality must be reversed, i.e. "less than" becomes "greater than", and "less than or equal to" becomes "greater than or equal to".Actually, from a purist's sense, the reversal rule also applies with equations. Its just that the reversal of "equals" is still "equals". The same goes for "not equal to".

it often simplifies arithmetic

Bogomol'nyi-Prasad-Sommerfield bound is a series of inequalities for solutions. This set of inequalities is useful for solving for solution equations.

Study everything - that's your best bet. Important subjects probably include: Polynomials, Exponents, Radicals, Solving Equations, Solving Inequalities, Absolute Value Equations and Inequalities, Lines, Word Problems, Systems of Equations (2x2's), Factoring, Division of Polynomials, Quadratics, Parabolas, Complex Numbers, Algebraic Fractions, Functions

Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.

It makes it allot less confusing. But, that is just my opinion.

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Just keep doing the same thing to both sides of the equation at every step.

Mainly, in the case of simple inequalities, you have to remember that when multiplying or dividing by a negative number, the direction of the inequality changes, for example, from greater-than to less-than or vice versa. Also, for more complicated inequalities, such as those that involve polynomials or absolute values, additional steps are required.

Equations can be tricky, and solving two step equations is an important step beyond solving equations in one step. Solving two-step equations will help introduce students to solving equations in multiple steps, a skill necessary in Algebra I and II. To solve these types of equations, we use additive and multiplicative inverses to isolate and solve for the variable. Solving Two Step Equations Involving Fractions This video explains how to solve two step equations involving fractions.

Even if you keep the decimal, later on you will still have to remove it. It is just an easier way to solve the equation.

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