What is the combining like terms property of equality in the proof process?
I’m trying to solve my equation with the properties of equality and I can’t figure out what this one is
The combining like terms property of equality states that when solving an equation, you can combine terms that have the same variable and exponent on both sides of the equation. This is done by adding or subtracting these terms.
For example, if you have the equation 2x + 3 = 5x - 2, you can use the combining like terms property to simplify it by rearranging the equation and grouping the x terms:
2x - 5x = -2 - 3
Simplifying further:
-3x = -5
This property allows you to simplify the equation by combining like terms, making it easier to solve for the variable.
The combining like terms property of equality is a step in the proof process that allows you to simplify an equation by combining similar terms on both sides of the equation. It is used when you have terms with the same variable raised to the same power and you want to simplify the equation by adding or subtracting those terms.
To explain it further, let's consider an example equation:
2x + 3x = 10
In this equation, "2x" and "3x" are like terms because they both have the variable "x" raised to the first power. To combine these terms, you add their coefficients (the numbers in front of the variable) and keep the variable the same:
(2 + 3)x = 10
5x = 10
By combining the like terms "2x" and "3x," we simplified the equation to "5x = 10" by applying the combining like terms property of equality.
This property is helpful because it allows you to simplify equations and make them easier to solve. However, it's important to note that you can only combine terms that have the exact same variable and the exact same exponent.