Given is 2(x+3)=10 so what is 2x+6=10 is it associative property of addition, commutative property of addition, multiplicative property of equality or distributive property if multiplication over addition
The given equation is: 2(x + 3) = 10.
To simplify this equation, you can start by applying the distributive property of multiplication over addition, which states that a(b + c) = ab + ac.
Using the distributive property, we can rewrite the equation as:
2 * x + 2 * 3 = 10.
Simplifying further, we have:
2x + 6 = 10.
Therefore, the equation 2x + 6 = 10 is the result after simplifying the given equation using the distributive property of multiplication over addition.
The statement 2(x+3) = 10 is an equation that represents a mathematical relationship, not a property. It is an equation that can be simplified to solve for the value of x.
Starting with 2(x+3) = 10:
Using the distributive property of multiplication over addition, we can distribute the 2 to both terms inside the parentheses:
2 * x + 2 * 3 = 10
Simplifying further:
2x + 6 = 10
Now, 2x + 6 = 10 is the simplified form of the equation. It is not an associative property of addition, commutative property of addition, multiplicative property of equality, or distributive property.
To solve for x, we can isolate the variable by subtracting 6 from both sides:
2x + 6 - 6 = 10 - 6
2x = 4
Finally, dividing both sides by 2 gives us the solution for x:
2x/2 = 4/2
x = 2
To determine whether the equation 2x + 6 = 10 involves the associative property of addition, commutative property of addition, multiplicative property of equality, or distributive property of multiplication over addition, let's go through each property and check which one applies.
1. Associative Property of Addition:
This property states that the way in which numbers are grouped when they are added does not affect the sum. However, in the equation 2x + 6 = 10, there is no addition involving grouping of numbers, so the associative property of addition does not apply here.
2. Commutative Property of Addition:
This property states that the order of numbers does not affect the sum when they are added. In the equation 2x + 6 = 10, there is no reordering of numbers involved in addition, so the commutative property of addition does not apply.
3. Multiplicative Property of Equality:
This property states that if two quantities are equal, then multiplying both sides by the same non-zero number will still yield equal quantities. In the equation 2(x + 3) = 10, multiplying both sides by 2 gives 2x + 6 = 20, not 2x + 6 = 10. Therefore, the multiplicative property of equality is not applicable here.
4. Distributive Property of Multiplication over Addition:
This property states that when multiplying a number by a sum, you can distribute the multiplication across each term of the sum. In the given equation 2(x + 3) = 10, we can use the distributive property to simplify the equation. Distributing the 2 to both x and 3, we get 2x + 6 = 10, which matches the equation we are trying to identify. Therefore, the equation 2x + 6 = 10 involves the distributive property of multiplication over addition.
In conclusion, the answer is: The equation 2x + 6 = 10 involves the distributive property of multiplication over addition.