Item 14 A student solves the inequality −6v>42. Each step in the student's solution is shown below. Identify where the student made any errors.

Step-by-step explanation:

Given the inequality solved by a student expressed as:

-6v>42

To get v, follow the simple steps

Step 1: multiply both sides by -1

-6v>42

-1(-6v)<-1(42)

6v < 42 (Note that when you multiply both sides of an inequality by a negative sign, the inequality sign will change)

Step 2: Divide through by 6

6v < 42

6v/6 < 42/6

v < 7

Hence the range of values of v are the values of v less than 7

Since we are not  given the options, you can compare the solution given with that of the student to figure out the error. The major error that may happen is the different not changing the inequality sign after multiplying or dividing with a negative value as shown.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!