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Why are the properties of equality important in solving equations?
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Why do you use the addition property of equality?
Why? - Mainly to help in solving equations.
2 What properties do you use when solving a one-step equation?
You often need the additive property of equality. It says if a=b then a+c=b+c.This alone may be enough to solve many equations. Sometimes you need to multiply or divide both sides. This is the multiplicative property of equality.
Why is it important to know various techniques for solving systems of equations and inequalities?
It is important to know several techniques for solving equations and inequalities because one may work better than another in a particular situation.
Addition property of equality?
If x=y then x+z=y+z or If x=y and a=b then x+a=y+b The formal name for the property of equality that allows one to add the same quantity to both sides of an equation. This, along with the multiplicative property of equality, is one of the most commonly used properties for solving equations.
What is one important difference between solving equations and solving inequalities?
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".
Why do you use the addition property of equality?
Why? - Mainly to help in solving equations.
2 What properties do you use when solving a one-step equation?
You often need the additive property of equality. It says if a=b then a+c=b+c.This alone may be enough to solve many equations. Sometimes you need to multiply or divide both sides. This is the multiplicative property of equality.
How do you solve two-step equations with fractions?
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.
Why is it important to know various techniques for solving systems of equations and inequalities?
It is important to know several techniques for solving equations and inequalities because one may work better than another in a particular situation.
When solving equations how do you justify your steps?
You should state the property used, such as distributive property of multiplication over addition or addition property of equality, etc.
Addition property of equality?
If x=y then x+z=y+z or If x=y and a=b then x+a=y+b The formal name for the property of equality that allows one to add the same quantity to both sides of an equation. This, along with the multiplicative property of equality, is one of the most commonly used properties for solving equations.
How are the rules for solving inequalities similar to those for solving equations?
Solving inequalities and equations are the same because both have variables in the equation.
Are trigonometric identities important?
Yes. Trigonometric identities are extremely important when solving calculus equations, especially while integrating.
How is solving an equality the same as solving an equation?
An equality and equation are essentially the same thing. The equality between two expressions is represented by an equation (and conversely).
What is one important difference between solving equations and solving inequalities?
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".
How is the multiplication or division property of equality used in the elimination method and are the properties always needed?
If you multiply or divide an equation by any non-zero number, the two sides of the equation remain equal. This property is almost always needed for solving equations in which the variables have coefficients other than 1.
What is a method for solving a system of linear equations in which you multiply one or both equations by a number to get rid of a variable term?
It is called solving by elimination.
