Help me, please. Thank you! Show step-by-step solution.

Linear Inequality:

1. You can work no more than 10 hours each week at your two jobs. Housecleaning pays 100 per hour and your sales job pays 150 per hour. How many hours do you need to work in each of your jobs to earn at least 1,000 each week to pay your bills? Explain how you arrived at that answer.

2. Joyce is making Christmas decors out of recycled materials that she would sell and use the proceeds to donate to a charitable institution. She would like to make at least 1500 in sales. She estimates that she will sell at most 100 pieces of Christmas decors. The Christmas balls that she is selling cost 20 each and the parol cost 30 each. Give two possible combinations of Christmas balls and parol that can be sold in order for Jenny to meet her goal. Justify your answer.

Linear Function:

1. Rose and her friends are out for vacation and rented a car that charges 1,000 per day plus 300 per mile traveled. They spend 2000 on car rental per day. If they traveled 30 miles on the first day, is their budget enough to pay for the car rental? Justify your answer.

2. A school had 1700 students enrolled in the year of 2010 and 2100 students in the year of 2016. If the student population (P) grows as a linear function of time t, where t is the number of years after the year of 2010. How many students will be enrolled in the school in 2022? Explain how you arrived to your answer.

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: