Write the absolute value equations in the form x−b =c (where b is a number and c can be either number or an expression) that have the following solution sets: Two solutions: x=−2, x=−32.

  |x +17| = 15

Step-by-step explanation:

The absolute value equation ...

  |x -b| = c

can be rewritten as two equations:

  x -b = -c

  x -b = c

The solution to the first is x = b -c.

The solution to the second is x = b +c.

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The first solution is the smaller of the two, so we have ...

  b -c = -32

  b +c = -2

Adding these two equations gives ...

  2b = -34   ⇒   b = -17

Subtracting the first equation from the second gives ...

  2c = 30   ⇒   c = 15

The the equation you seek is ...

  |x +17| = 15

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!