Properties of Equality: Addition
Properties of equality are used to perform operations on both sides of an equation while maintaining its equality
Properties of equality are used to perform operations on both sides of an equation while maintaining its equality. Addition is one of the properties of equality that enables us to add the same number to both sides of an equation without changing its solution.
The property of equality states that if a = b, then a + c = b + c.
In other words, adding the same number to both sides of an equation preserves the equality between the two sides.
To illustrate the usage of the property of equality with addition, let’s consider the following example:
Example 1: Solve the equation 2x + 5 = 10.
To solve this equation, we need to isolate the variable, x.
To do that, we can use the property of equality by adding -5 (the additive inverse of 5) to both sides of the equation:
2x + 5 – 5 = 10 – 5
Simplifying both sides, we get:
2x = 5
Now, we can divide both sides of the equation by 2 to solve for x:
2x/2 = 5/2
x = 2.5
Hence, the solution to the equation 2x + 5 = 10 is x = 2.5.
The property of equality with addition is handy in solving various types of equations, such as linear equations, quadratic equations, and exponential equations. It allows us to manipulate the equation by adding or subtracting the same value from both sides, ultimately simplifying the equation or isolating the variable.
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