SOLUTION: -5|x - 3| - 5 < 15 Can you show the steps in solving this? Thanks

Question 1058951: -5|x - 3| - 5 < 15
Can you show the steps in solving this? Thanks
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Solve first for the absolute value expression, and then deal with solving the actual variable inside.

Let .

, do you understand this step?

Now you solve for two possibilities.

Just showing steps without explanation:
--

-

-
Put those together:

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

-5|x - 3| - 5 < 15
Can you show the steps in solving this? Thanks

Looking at the left side of the inequality, it's obvious that it will be negative (< 0), regardless of what value you enter for x, and a negative value WILL ALWAYS be < 15.
Therefore, the solution is:
As a matter of fact, the smallest value that you can substitute for x to get the LARGEST value on the left-side of the inequality, is 3.
With x = 3, we get: - 5(0) - 5 < 15, or - 5 < 15. There you have it! The LARGEST value on the left-side (- 5) is still < 15.
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
-5|x - 3| - 5 < 15
Can you show the steps in solving this? Thanks
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solution for this equation is the entire set of real numbers.

Any real number is a solution.

Left side is always negative. Right side is always positive.
Left side is always less than the right side.
The inequality is satisfied for all x.
For any x.

Writing by "josgarithmetic" is absolutely wrong. Disregard it.

>>> "josgarithmetic", STOP, at last, to write NONSENSE. <<<

Plot y = -5|x - 3| - 5 (red) and y = 15 (green)

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