Question 9 (2 points)
For the equation: 2(x - 7) = 3 - 7x + 5 + 8 + 7x + 11 , the right side of the equation can be simplified by combining like terms.
Simplify the right side of the equation:
The left side of the equation can be simplified using the Distributive Property.
Simplify the left side of the equation: 2x-14
Word Bank:
36x 2x-5 27x 6x+30 2x-14 27 2x+14 30
Blank 1:
Blank 2:
2x-14
Blank 1: 36x
Blank 2: 30
13. The speed limit sign on the expressway says that the speed limit is 55 mph. Write an inequality that represents all speeds you can legally drive on the expressway. (1 point)
Responses
Blank 1: 2x-14
Blank 2: 36x
To simplify the right side of the equation, we need to combine like terms.
The right side of the equation is:
3 - 7x + 5 + 8 + 7x + 11
To combine like terms, we add or subtract the coefficients of variables that have the same power.
Here, we can combine the constants (numbers without variables) 3, 5, 8, and 11 to get:
3 + 5 + 8 + 11 = 27
Next, we can combine the terms with x. We have -7x and +7x. Since the coefficients are opposites, they cancel each other out: -7x + 7x = 0.
So the right side of the equation simplifies to:
27
Therefore, Blank 1 is: 27.
Now let's simplify the left side of the equation, which is 2(x - 7):
To simplify the left side, we need to apply the Distributive Property, which states that:
a(b + c) = ab + ac
In this case, a = 2, b = x, and c = -7.
Using the Distributive Property, we multiply 2 by both x and -7:
2(x - 7) = 2x - 14
So the left side of the equation simplifies to:
2x - 14
Therefore, Blank 2 is: 2x - 14.
Putting it all together, the simplified equation becomes:
2x - 14 = 27