Question 1192919
see my worksheet below.
see my comments below the worksheet.


<img src = "http://theo.x10hosting.com/2022/040401.jpg" >


the basic definition of absolute value is:


abs(x) = x, if x is positive.
abs(x) = -x, if x is negative.


by x, they mean the expression within the absolute value sign.
for example:
abs(x-3) is equal to (x-3), if the expression (x-3) is positive.
abs(x-3) is equal to -(x-3), if the expression (x-3) is negative.


so you have to break up abs(x-3) into two parts.
the first part is (x-3).
the second part is -(x-3).


that's the concept behind solving this problem.
my worksheet does that.
it breaks the problem up into:
++ ----- (x-3) + 4(x+2) > 17
-- ----- -(x-3) - 4(x+2) > 17
+- ----- (x-3) - 4(x+2) > 17
-+ ----- -(x-3) + 4(x+2) > 17
and solves each one separately.
the solutions were:
x > 2.4
x < -4.4
x < -9.3
x > 2
x > 2.4 is superfluous because it's covered by x > 2.
x - 9.3 is superfluous because it's covered by x < 4.4.
x > 2 or x < 4.4 are your solutions.


i graphed the equation of abs(x-3) + 4 * abs(x+2) = y and y = 17 to show you how that looks graphically.
that's shown below.


<img src = "http://theo.x10hosting.com/2022/040402.jpg" >


let me know if you have any questions.
theo