How are algebraic properties used to justify method for solving a one variable equation?

Subject- Math

Time/Date This Question Was ANswered- On Wednesday, April 29th in the year 2020, at 10:11AM

Question- How are algebraic properties used to justify method for solving a one variable equation?

Answer- An equation is a mathematical statement that two expressions are equal. An equation will always contain an equal sign with an expression on each side. Expressions are made up of terms, and the number of terms in each expression in an equation may vary.  Algebraic equations contain variables, symbols that stand for an unknown quantity. Variables are often represented with letters, like x, y, or z. Sometimes a variable is multiplied by a number. This number is called the coefficient of the variable. For example, the coefficient of 3x is 3. An important property of equations is one that states that you can add the same quantity to both sides of an equation and still maintain an equivalent equation. Sometimes people refer to this as keeping the equation “balanced”. If you think of an equation as being like a balance scale, the quantities on each side of the equation are equal, or balanced.  Let’s look at a simple numeric equation, 3 + 7 =10, to explore the idea of an equation as being balanced.  The expressions on each side of the equal sign are equal, so you can add the same value to each side and maintain the equality. Let’s see what happens when 5 is added to each side.

3 + 7 + 5 = 10 + 5

Since each expression is equal to 15, you can see that adding 5 to each side of the original equation resulted in a true equation. The equation is still “balanced.”  On the other hand, let’s look at what would happen if you added 5 to only one side of the equation.

3 + 7 = 10

3 + 7 + 5 = 10

15 ≠ 10

Adding 5 to only one side of the equation resulted in an equation that is false. The equation is no longer “balanced”, and it is no longer a true equation! Addition Property of Equality

. For all real numbers a, b, and c: If a = b, then a + c = b + c.  If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you isolate the variable. Isolating the variable means rewriting an equivalent equation in which the variable is on one side of the equation and everything else is on the other side of the equation.  When the equation involves addition or subtraction, use the inverse operation to “undo” the operation in order to isolate the variable. For addition and subtraction, your goal is to change any value being added or subtracted to 0, the additive identity.

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