QuestionSolve the equation $-8|-5 x+9|=9$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $-8|-5x+9|=9$ . The absolute value of a number is its distance from zero on the number line, and is always non-negative.
3. We will solve the equation by isolating the absolute value expression and then splitting the equation into two cases one for the positive value and one for the negative value.

STEP 2

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the equation by -8.
$|-5x+9| = -\frac{9}{8}$

STEP 3

The absolute value of a number can never be negative, so there are no solutions to the equation $|-5x+9| = -\frac{9}{8}$ .
Therefore, the equation $-8|-5x+9|=9$ has no solutions.

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