Brainliest + MAJOR POINTS!

Checking account earnings at Money’s Bank are expressed by the equation,
I= −0.12x+7.5I
The earnings at Common Cent’s Bank are modeled by I=−0.82x+8.9I

In both cases, x is the number of checks written.
For what range of checks will a checking account at Common Cent’s Bank generate more earnings income than one at Money's Bank? Show your work or explain how you got your answer.

So, we need to find when the Common Cent's Bank account will be GREATER than the Money's Bank. We know that the Money's Bank is the first question, and that the Common Cent's Bank account is the second one. (I don't know what the | is for at the end, so I'll just ignore it). Now we need to find out when one is GREATER than the other, so we will use an inequality.

-0.82x+8.9 > -0.12x+7.5

Now that we have this, we simple solve for x. First step will be to bring -0.12x to the other side, creating

-0.82x+8.9+0.12x > -0.12x+7.5

-0.70x+8.9 > 7.5

Now, we will bring the constants to the other side. In this case, put 8.9 to the right side by subtracting from both sides.

-0.70x+8.9-8.9 > 7.5-8.9

-0.70x > -1.4

Now that we have that, we will divide both sides by -0.70. Don't forget, when dividing by a negative number, always flip the inequality sign (> to <)

-0.7x/-0.7 < -1.4/-0.7

x < 2

So, the range in which they have to right checks to make more money will be if they right less than 2 checks.