Use the definition of absolute value,
![|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}](https://tex.z-dn.net/?f=%7Cx%7C%20%3D%20%5Cbegin%7Bcases%7D%20x%20%26%20%5Ctext%7Bif%20%7D%20x%20%5Cge%200%20%5C%5C%20-x%20%26%20%5Ctext%7Bif%20%7D%20x%20%3C%200%20%5Cend%7Bcases%7D)
If x - 1 ≥ 0, then |x - 1| = x - 1, and so
|x - 1| = 5x + 2
x - 1 = 5x + 2
4x = -3
x = -3/4
Otherwise, if x - 1 < 0, then |x - 1| = -(x - 1), which means
|x - 1| = 5x + 2
-x + 1 = 5x + 2
6x = -1
x = -1/6
3x : 2 = 15
3x = 15 * 2
3x = 30
x = 30 : 3
x = 10
--------------------------------
3(10) :2 = 15
Answer:
x=-5/3
Step-by-step explanation:
ABD + DBC = ABC
Substitute the values
6x+9 + x+1 = 10x+15
Combine like terms
7x+10 = 10x+15
Subtract 7x from each side
7x-7x+10 = 10x-7x+15
10 = 3x+15
Subtract 15 from each side
10-15 = 3x+15-15
-5 =3x
Divide each side by 3
-5/3 =x
This will give us a negative value for DBC
DBC = -5/3 +3/3 = -2/3
We cannot have a negative value for an angle
Check the values given.
Answer:
x = 30
y = 54
Step-by-step explanation:
You want the solution to the system of equations ...
- 2x +12 +2y = 180
- 4x +y +6 = 180
<h3>Solution</h3>
Divide the first equation by 2 and subtract the result from the second equation.
(4x +y +6) -(2x +12 +2y)/2 = (180) -(180)/2
3x = 90 . . . . . . . simplify
x = 30 . . . . . . . . divide by 3
4(30) +y +6 = 180 . . . . substitute into the second equation
y = 180 -126 = 54
The values of x and y are ...
x = 30
y = 54
__
<em>Additional comment</em>
A suitable graphing calculator can find the solution using the equations "as is."
Answer:
60
Step-by-step explanation:
You have five exterior choices, then you multiply that by the six interior choices, then multiply the two model choices.