What property justifies that 6x+9/3=2x+3? A. Commutative Property of Addition B. Commutative Property of Multiplication C. Distributive Property D. Addition of Like Terms
I'm not sure how to do this. Please help!
Is it C?
so what ?
To determine which property justifies the equation, let's break down the properties and see which one applies here:
A. Commutative Property of Addition: This property states that you can change the order of numbers being added without affecting the result. For example, a + b = b + a.
B. Commutative Property of Multiplication: This property states that you can change the order of numbers being multiplied without affecting the result. For example, a × b = b × a.
C. Distributive Property: This property states that multiplication can be distributed over addition or subtraction. For example, a × (b + c) = a × b + a × c.
D. Addition of Like Terms: This property states that terms with the same variables and exponents can be combined by adding their coefficients. For example, 2x + 3x = (2 + 3)x = 5x.
Now, let's look at the given equation: 6x + 9/3 = 2x + 3.
To simplify, let's start by simplifying the right-hand side of the equation. We can combine the like terms 2x and 3 to get 5x.
Now the equation becomes: 6x + 9/3 = 5x + 3.
Next, let's simplify the left-hand side of the equation. We can simplify 9/3 to 3.
Now the equation becomes: 6x + 3 = 5x + 3.
Notice that the equation remains the same even after rearranging the terms. We can subtract 3 from both sides of the equation to isolate the variable.
Now the equation becomes: 6x = 5x.
Since the equation is still true even after rearranging the terms, the property that justifies this equation is the D. Addition of Like Terms.
Therefore, the correct answer is D. Addition of Like Terms.
you are correct
1/3 (6x+9) = 1/3 * 6 + 1/3 * 9 = 2x+3