For the equation 2(x−5)=9−3x+6+8+3x+7
, the left side of the equation can be simplified using the Distributive Property, and the right side of the equation can be simplified by combining like terms. (2 points)
First, let's simplify the left side of the equation using the Distributive Property:
2(x-5) = 2 * x - 2 * 5 = 2x - 10.
Now let's simplify the right side of the equation by combining like terms:
9 - 3x + 6 + 8 + 3x + 7 = (9 + 6 + 8 + 7) - 3x + 3x = 30.
So the simplified equation is 2x - 10 = 30.
To simplify the left side of the equation 2(x−5), we need to apply the Distributive Property. This property states that we need to multiply each term inside the parentheses by the number outside the parentheses.
Therefore, 2(x−5) becomes 2 * x - 2 * 5, which simplifies to 2x - 10.
Now let's simplify the right side of the equation. The right side expression is 9-3x+6+8+3x+7. We can combine the like terms that have x and the constant terms separately.
For the x terms, we have -3x and +3x. When we combine these terms, -3x + 3x becomes zero, so they cancel each other out.
For the constant terms, we have 9, 6, 8, and 7. When we add them together, 9 + 6 + 8 + 7 equals 30.
Therefore, the right side of the equation simplifies to 30.
Now we can rewrite the equation with the simplified expressions:
2x - 10 = 30
This is the simplified form of the equation, where the left side has been simplified using the Distributive Property and the right side has been simplified by combining like terms.