Catie is starting a babysitting business. she spent $26 to make signs and flyers to advertise. she charges an initial fee of $5 and then $3 for each hour of service. write and solve an inequality to find the number of hours she will have to babysit to make a profit.

When you're solving for inequalities, you're looking for the relative size of two values meaning something is less than, greater than something else. In this case, Catie is looking to make a profit more than (>) her cost. So: 

Step 1: $5 (initial fee) + $3/h of service thereafter > $26 (cost of advertising) 
                                                                                                
Step 2:   -5                                                                     -5
         
Step 3:                        + $3/h of service thereafter > $26 (cost of advertising) 
                                                                                 
                                          3                                          3
Step 4:  h = 7

Therefore, in 7 hours, Catie will have enough money to breakeven. But we are looking for profit. So, in the 8th hour, Catie will have enough to make a profit.  

The inequality can be written as so: 5+3h>26 

You can also look at it another way: 

Hour 1: $5 (initial fee) + $3/h thereafter = 8
Hour 2: +3 = 11 
Hour 3: +3 = 14
Hour 4: +3 = 17
Hour 5: +3 = 20
Hour 6: +3 = 23
Hour 7: +3 = 26 (Breakeven) 
Hour 8: +3 = 29 (Profit) 
     

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