Properties of Equality: Addition
Properties of equality in mathematics are rules that allow us to perform operations on both sides of an equation without changing its solution
Properties of equality in mathematics are rules that allow us to perform operations on both sides of an equation without changing its solution. One of these properties is the addition property of equality.
The addition property of equality states that if we have an equation, and we add the same value to both sides of the equation, the equality still holds.
In symbol form, if a = b, then a + c = b + c, where a, b, and c are any real numbers.
For example, let’s say we have the equation 3x = 9. To solve for x, we can use the addition property of equality.
Step 1: 3x = 9
Step 2: We want to isolate x, so we can add the same value to both sides of the equation. Let’s add 2 to both sides:
3x + 2 = 9 + 2
Step 3: Simplify both sides by performing the addition:
3x + 2 = 11
Now, we have a new equation that is equivalent to the original equation. We can continue solving for x by using other algebraic techniques, but the important point is that we maintained equality throughout the process by applying the addition property of equality.
It’s important to remember that the value we add to both sides can be any real number. This property allows us to transform equations and make them more manageable or easier to solve.
In summary, the addition property of equality allows us to add the same value to both sides of an equation without changing its solution. This property is a fundamental concept in algebra and is an essential tool for solving equations.
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