SOLUTION: can you please show me how to solve this problem? -2|3x-4|<16 thank you

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Question 408765: can you please show me how to solve this problem? -2|3x-4|<16
thank you
Found 2 solutions by jim_thompson5910, richard1234:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
If you divide both sides of the inequality by -2 you'll get

|3x-4| > -8

Note: remember that the sign will flip when you divide both sides by a negative number.

Now remember that the absolute value of ANY number is ALWAYS nonnegative. In other words, it will NEVER be negative.

Since 0 and every positive number is greater than any negative number, this means that the inequality |3x-4| > -8 is true for ALL values of x.

So there are an infinite number of solutions. Basically, any real number will work for x.

If you need more help, email me at jim_thompson5910@hotmail.com

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Jim

Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website!
Dividing both sides by -2, we obtain

(don't forget to switch the inequality sign). However, since for all real x, then for all x,

so all real numbers x satisfy.

When you learn about complex numbers you'll see that all complex solutions satisfy. However doesn't denote absolute value anymore, it denotes the magnitude of the number (similar to absolute value, but in two dimensions).