Solve: -10(x - 1) = 10 - 10x a) no solution b) x = -1 c) x = 0 d) infinitely many solutions

The answer is D because:

-10 (x - 1) = 10 - 10x
-10x + 10 = 10 - 10x
-10x + 10x = 10 - 10
0x = 0

fil in x = 1 --> 0 * 1 = 0 : 0 = 0
fil in x = 2 --> 0 * 2 = 0 : 0 = 0
etc.

See a solution process below:
Explanation:
Let's call the number of miles driven we are looking for
m
.
The the total cost of ownership for the first car model is:
12000
+
0.1
m
The the total cost of ownership for the second car model is:
14000
+
0.08
m
We can equate these two expressions and solve for
m
to find after how many miles the total cost of ownership is the same:
12000
+
0.1
m
=
14000
+
0.08
m
Next, we can subtract
12000
and
0.08
m
from each side of the equation to isolate the
m
term while keeping the equation balanced:
−
12000
+
12000
+
0.1
m
−
0.08
m
=
−
12000
+
14000
+
0.08
m
−
0.08
m
0
+
(
0.1
−
0.08
)
m
=
2000
+
0
0.02
m
=
2000
Now, we can divide each side of the equation by
0.02
to solve for
m
while keeping the equation balanced:
0.02
m
0.02
=
2000
0.02
0.02
m
0.02
=
100000
After 100,000 miles the total cost of ownership of the two cars would be the same.