[MUSIC] Let's work with linear inequality word problems.

[SOUND] Rachel is a saleswoman. She receives a salary of $45,000 per

year. In addition, she receives 7% of her sales

amount for the year. What are the sales amounts that will

allow her to earn more than $56,900 per year? So we want Rachel's earnings to be

more than, just greater than $56,900. Well, what are these earnings? We're told

that she receives a base salary of $45,000, but then also 7% for her sales

amount for the year. That is her earnings or the base salary

plus 7% or .07 of means times her sales amount.

So let's let x equal Rachel's annual sales amount.

Therefore, her earnings here would be the base salary, 45,000, plus 7% of x, and

putting that in here, gives us the following inequality: 45,000 plus .07x

needs to be greater than 56,900. And now we can subtract 45,000 from each

side, which gives us 07. times x greater than 56,900 minus 45,000.

Or .07x greater than 11,900. And now we can divide both sides by 07.,

whihc gives us x greater than 11,900 divided by .07.

Now what is this number here? Let's compute that.

So it's 11,900 divided by .07 is equal to 11,900 divided by 7 divided 100, which is

equal to 11,900 times 100 divided by 7. And then 7 goes into 11,900 1700 times.

Therefore, this is equal to 170,000, and putting that back in here,

that means as long as x, which is Rachel's annual sales amount, is larger

than $170,000, indeed, she'll be earning more than

$56,900 per year. And this is how we work with linear

inequality word problems. Thank you, and we'll see you next time.

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