How do you solve 6 + 8 x &lt; 2 ( - 3 + 4 x ) ?

Question

How do you solve       6    +    8    x    &amp;lt;    2          (      -      3      +      4      x      )       ?

Campasenabs · Accepted Answer

Step 1Your goal here is to isolate x on one side of the inequality.      6    +    8    x    &amp;lt;    2    ⋅          (      -      3      +      4      x      )      Expand the parenthesis to get      6    +    8    x    &amp;lt;    2    ⋅          (      -      3      )        +    2    ⋅    4    x        6    +    8    x    &amp;lt;    -    6    +    8    x  Now, notice what happens when you subtract       8    x   from both sides of the inequality      6    +                                                                      8                x                                                          -                                                                      8                x                                                          &amp;lt;    -    6    +                                                                      8                x                                                          -                                                                      8                x                                                              6    &amp;lt;    -    6  When is 6 smaller than -6?Never, which implies that this inequality has no real solutions. In other words, regardless of the value of x you plug in, the left side of the original inequality will never be smaller than the right side.      6    +    8    x                                                                      &amp;lt;                                                          2    ⋅          (      -      3      +      4      x      )        ,                                     (      ∀      )        x    ∈    ℝ  Therefore, you can say that       x    ∈    ∅   .

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