Answer:
2.(b) w= 3
3. x= -3 or x= 3
Step-by-step explanation:
2.(b) <u>Method 1:</u>
![\frac{2w - 1}{5} + w + 2 = 2w \\ \frac{2w - 1}{5} = 2w - w - 2 \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B2w%20-%201%7D%7B5%7D%20%20%2B%20w%20%2B%202%20%3D%202w%20%5C%5C%20%20%5Cfrac%7B2w%20-%201%7D%7B5%7D%20%20%3D%202w%20-%20w%20-%202%20%5C%5C%20)
Simplify:
![\frac{2w - 1}{5} = w - 2](https://tex.z-dn.net/?f=%20%5Cfrac%7B2w%20-%201%7D%7B5%7D%20%20%3D%20w%20-%202)
×5 on both sides:
![2w - 1 = 5(w - 2)](https://tex.z-dn.net/?f=2w%20-%201%20%3D%205%28w%20-%202%29)
Expand:
![2w - 1 = 5w - 10](https://tex.z-dn.net/?f=2w%20-%201%20%3D%205w%20-%2010)
Bring constants to 1 side, w terms to the other:
![5w - 2w = 10 - 1](https://tex.z-dn.net/?f=5w%20-%202w%20%3D%2010%20-%201)
Simplify:
![3w = 9](https://tex.z-dn.net/?f=3w%20%3D%209)
Divide both sides by 3:
![w = 9 \div 3 \\ w = 3](https://tex.z-dn.net/?f=w%20%3D%209%20%5Cdiv%203%20%5C%5C%20w%20%3D%203)
<u>Method 2:</u>
![\frac{2w - 1}{5} + w + 2 = 2w](https://tex.z-dn.net/?f=%20%5Cfrac%7B2w%20-%201%7D%7B5%7D%20%20%2B%20w%20%2B%202%20%3D%202w)
Multiply by 5 throughout:
![2w - 1 + 5(w + 2) = 5(2w)](https://tex.z-dn.net/?f=2w%20-%201%20%20%2B%205%28w%20%2B%202%29%20%3D%205%282w%29)
Expand:
![2w - 1 + 5w + 10 = 4w](https://tex.z-dn.net/?f=2w%20-%201%20%2B%205w%20%2B%2010%20%3D%204w)
Simplify:
![7w - 9 = 4w](https://tex.z-dn.net/?f=7w%20-%209%20%3D%204w)
+9 on both sides:
![7w = 4w + 9](https://tex.z-dn.net/?f=7w%20%3D%204w%20%2B%209)
-4w on both sides:
![7w - 4w = 9](https://tex.z-dn.net/?f=7w%20-%204w%20%3D%209)
Simplify:
![3w = 9](https://tex.z-dn.net/?f=3w%20%3D%209)
Divide by 3 on both sides:
![w = 3](https://tex.z-dn.net/?f=w%20%3D%203)
3. ![\frac{6x - 12}{3} + 4 = \frac{18}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6x%20-%2012%7D%7B3%7D%20%20%2B%204%20%3D%20%20%5Cfrac%7B18%7D%7Bx%7D%20)
Multiply by 3x on both sides:
![\frac{3x(6x - 12)}{3} + 3x(4) = \frac{3x(18)}{x} \\ x(6x - 12) + 12x = 3(18)](https://tex.z-dn.net/?f=%20%5Cfrac%7B3x%286x%20-%2012%29%7D%7B3%7D%20%20%2B%203x%284%29%20%3D%20%20%5Cfrac%7B3x%2818%29%7D%7Bx%7D%20%20%5C%5C%20%20x%286x%20-%2012%29%20%2B%2012x%20%3D%203%2818%29)
Expand:
![x(6x) - x(12) + 12x = 54 \\ 6x^{2} - 12x + 12x = 54 \\](https://tex.z-dn.net/?f=x%286x%29%20-%20x%2812%29%20%2B%2012x%20%3D%2054%20%5C%5C%206x%5E%7B2%7D%20%20-%2012x%20%2B%2012x%20%3D%2054%20%5C%5C)
Simplify:
![6 {x}^{2} = 54](https://tex.z-dn.net/?f=6%20%7Bx%7D%5E%7B2%7D%20%20%3D%2054)
Divide by 6 on both sides:
![{x}^{2} = 9](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%209)
-9 on both sides:
![{x}^{2} - 9 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%209%20%3D%200)
Factorise:
*Since a²-b²= (a +b)(a -b),
![{x}^{2} - {3}^{2} = 0 \\ (x + 3)(x - 3) = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%20%20%7B3%7D%5E%7B2%7D%20%20%3D%200%20%5C%5C%20%28x%20%2B%203%29%28x%20-%203%29%20%3D%200)
Thus,
x +3= 0 or x -3= 0
x= -3 or x= 3
Answer:
-10y+42.
Step-by-step explanation:
Distribute.
8y-18y+42
-10y+42
:D I hope this helped you!
Answer:
The x-intercepts of a function are found where the graph of a function crosses the x-axis on a pair of Cartesian coordinate axes. How to Find the X-intercepts of a Function The x-intercepts of a function f (x) is found by finding the values of x which make f (x) = 0. Write f (x) = 0, and solve for x to find the x-intercepts of a function.
Step-by-step explanation:
find the x-intercepts ans you will be able to answer the rest of the question then fill in the blanks
hope this helps :)
Answer:
14: 36
15: 17.5
16: 7.25
Step-by-step explanation:
The correct answer is B) the data is continuous because there are infinitely many values.
This does not mean that your gas tank holds an infinite amount of gas; it means that there is an infinite number of smaller fractions that we can break the amount of gas into. We can have 1/2 gallon, 1/4 gallon, 1/8, etc. continuing infinitely.