The equation p=100−5t represents the percent p of battery power remaining in a tablet after t hours. a. Identify the independent and dependent variables. Then describe how the battery power changes over time.

The independent variable is
and the dependent variable is
.

The battery power begins at
% and decreases
% each hour.

Here's why:

The 4 and 8 on the left side combine to 12. The 5x and -3x on the right hand side combine to 2x.

This means the equation for choice D becomes 2x+12 = 2x-12

From here, subtract 2x from both sides. Doing so will cancel each copy of 2x and the x terms go away entirely. We're left with 12 = -12 which is a false statement since we don't have the same number on both sides. We have a contradiction instead, so there are no solutions here.

No matter what we replace x with in equation D, it will always be false.

If you graphed y = 2x+12 and y = 2x-12, you would find that the lines are parallel. Parallel lines never intersect. Intersection points are solution points, so this is a visual way to see that we don't have any solutions.