Respuesta :
The absolute value [tex] |x| [/tex] always returns the "positive version" of a number.
This means that if the number is positive, the absolute value does nothing:
[tex] |x| = x [/tex]
And if the number is negative, the absolute value flips its sign:
[tex] |x| = -x [/tex]
So, if 8x+4 is positive, the inequality becomes
[tex] 8x+4 < 28 [/tex]
If 8x+4 is negative, the inequality becomes
[tex] -8x-4 < 28 \iff 8x+4 > -28 [/tex]
So, 8x+4 must be either a positive number smaller than 28, or a negative number greater than -28. It means that
[tex] -28 < 8x+4 < 28 [/tex]
Subtract 4 from all sides:
[tex] -32 < 8x < 24 [/tex]
Divide all sides by 8:
[tex] -4 < x < 3 [/tex]
