Question

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

Answer 1

x = -2/5 x = -4/5

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

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

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!