Question

What is the value of z in the equation 2(4z – 9 – 11) = 166 – 46?

Answer 1

Our current equation is:
2(4z - 9 - 11) = 166 - 46
First, let's simplify the right side of the equation.
166 - 146 = 120
Now, we have:
2(4z - 9 - 11) = 120

Since we have 2(4z - 9 -11), this side of the equation is looking for the "Distributive Property."
The Distributive Property allows any variable/number outside of a parenthesis to multiply by all inside numbers/variables.

For example:
3(1 + 2)
3(1) + 3(2)
3 + 6
9.


Now that we've explained what we're dealing with, let's distribute!

2(4z - 9 - 11)
2(4z) + 2(-9) + 2(-11)
Remember when you multiply a positive number by a negative, it becomes a negative product.
8z -18 -22 = 120
Combine like-terms.
-18 -22 = -40 (When subtracting a positive from a negative, you're essentially just adding two positive numbers with negative signs as the sum.)
We now have:
8z -40 = 20
Add 40 to both sides.
8z = 60
Divide both sides by 8 to solve for z.
8z / 8 = z
160 / 8 = 20

z = 20

I hope this helps!

Answer 2

2(4z-9-11)=166-46
8z-18-22=120
8z-40=120
Add 40 from both side
8z-40+40=120+40
8z=160
Divided 8 from both side
8z/8=160/8
z=20. Hope it help!