Question

Solve for all values of x in simplest form. 9-4|3+5x|=5

Answer 1

Answer:

x = -2/5                  x = -4/5

Step-by-step explanation:

9-4|3+5x|=5

Subtract 9 from each side

9-9-4|3+5x|=5-9

-4|3+5x|=-4

Divide by -4

-4/-4 |3+5x|=-4/-4

|3+5x|=1

The solution to an absolute value is positive and negative

3+5x =1            3+5x = -1

Subtract 3 from each side

5x = 1-3             5x = -1-3

5x = -2               5x = -4

Divide by 5

5x/5 = -2/5           5x/5 = -4/5

x = -2/5                  x = -4/5

Answer 2

Answer:

$x=-2/5\text{ or } x=-4/5$

Step-by-step explanation:

So we have the equation:

$9-4|3+5x|=5$

First, subtract 9 from both sides:

$-4|3+5x|=-4$

Divide both sides by -4:

$|3+5x|=1$

Definition of Absolute Value:

$3+5x=1\text{ or } 3+5x=-1$

Subtract 3 from both sides:

$5x=-2\text{ or } 5x=-4$

Divide both sides by 5:

$x=-2/5\text{ or } x=-4/5$

And we're done!