Solve each Inequality. Graph the solution set and write it using interval notation.

Question

|3x+4|<16

 

 

Show the solution☺️ Thanks in advance!

Answer 1

This can be converted to -16 <  3x+4 < 16

 

then -20 < 3x< 12  after subtracting 4 from all 3 parts

 

& finally, after dividing all 3 parts by 3:  -20/3 < x < 4

 

because it's a conjunction, this is the easiest method.

Answer 2

3x + 4 < 16            or             3x + 4 > -16

 

Solve the two-part inequality.

 

3x < 12                  or              3x > -20

 

x < 4                     or                x > -6.66

 

 

-6.66 < x < 4

 

 

To graph, draw a number line labeled -6.66 and 4.  On the number line, draw open circles at -6.66 and 4.  Then connect the two circles with a line.  That line represents the solution set.

 

Answer 3

3x + 4 < 16     or 3x +4 > -16

 

3x < 12    AND 3x > -20

 

x < 4  or x > -20/3

 

(-20/3 , 4)

 

open circle at -20/3; open circles at 4.

Shade in between

 

check:   

  x= -7 (should fail)   | 3(-7)+4 | < 16

                                | -21 + 4 | < 16

                                 | -17 | < 16

                                 17 < 16 <--- fails as expected

 

x = -3,-2,-1,zer0,1,2,3 work as expected

 

x = 5, fails as expected as | 3(5) + 4 | = | 15 + 4 | = |19| = 19 < 17 is false

 

The answer is checked, verified, and proven to be correct:

x < 4 or x > -20/3

(-20/3 , 4)