How to graph and solve | 2 x + 4 | &lt; 8 ?

Question

How to graph and solve             |      2      x      +      4      |        &amp;lt;    8  ?

Rory Hess · Accepted Answer

(1)      2    x    +    4    ≥    0    →    x    ≥    -    2   the absolute bars have no effect:      2    x    +    4    &amp;lt;    8    →    x    &amp;lt;    2  These two logically imply that       -    2    ≤    x    &amp;lt;    2  (2)      2    x    +    4    ≤    0    →    x    ≤    -    2   the absolute bars flip the signs      -    2    x    -    4    &amp;lt;    8    →   now add       2    x    +    4   on both sides:      0    &amp;lt;    8    +    2    x    +    4    →   now subtract       12  :      -    12    &amp;lt;    2    x    →    -    6    &amp;lt;    x    →    x    &amp;gt;    -    6  So       -    6    &amp;lt;    x    ≤    -    2  By combining the two numbers, the result is:       -    6    &amp;lt;    x    &amp;lt;    2  graph{|2x+4| [-13.53, 11.78, -2.08, 10.58]}

How to graph and solve | 2 x + 4 | < 8 ?

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