It is given that 2(3 + x) = 6 + 2x. This is an example of the ___________ property.
Responses
A associativeassociative
B commutativecommutative
C distributivedistributive
D identity
C distributive
are you sure
I apologize for the confusion. You are correct, the given equation is an example of the distributive property. Thank you for catching that mistake.
Solve for x.
5(x − 3) − 6(x − 2) > 8x + 2
Responses
A x > 59
x > 5 9
B x < 59
x < 5 9
C x > −59
x > − 5 9
D x < −59
x < − 5 9
E x > −95
To solve for x in the inequality 5(x − 3) − 6(x − 2) > 8x + 2, we can start by simplifying both sides of the inequality:
5x - 15 - 6x + 12 > 8x + 2
Combine like terms:
-x - 3 > 8x + 2
Now, let's isolate the variable x on one side of the inequality. We can do this by subtracting 8x from both sides:
-x - 8x - 3 > 2
Simplifying further:
-9x - 3 > 2
Next, we can add 3 to both sides of the inequality:
-9x > 5
To isolate x, we need to divide both sides by -9. However, remember that when dividing or multiplying an inequality by a negative number, the direction of the inequality sign flips:
x < 5/(-9)
Simplifying the expression on the right:
x < -5/9
Therefore, the correct answer is:
D x < - 5 9
This is an example of the distributive property.
To determine the property demonstrated in the given equation 2(3 + x) = 6 + 2x, we need to simplify both sides of the equation and compare them.
First, let's simplify the left side:
2(3 + x) = 6 + 2x
Distributing the 2 to both terms inside the parentheses:
6 + 2x = 6 + 2x
Now, we compare the left and right sides of the equation and observe that they are equal.
This means that the equation demonstrates the Distributive Property. Therefore, the correct answer is C - distributive.