What are the boundaries of x if 2 x - 1 x + 5 ≥ x + 2 x + 3 ?

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What are the boundaries of x if                     2        x        -        1                    x        +        5              ≥                  x        +        2                    x        +        3              ?

1s1zubv · Accepted Answer

Step 1      ⇒                  2        x        -        1                    x        +        5              -                  x        +        2                    x        +        3              ≥    0        ⇒                            (          2          x          -          1          )                          (          x          +          3          )                -                  (          x          +          2          )                          (          x          +          5          )                                      (          x          +          5          )                          (          x          +          3          )                      ≥    0        ⇒                  2                  x          2                +        5        x        -        3        -                  x          2                -        7        x        -        10                              (          x          +          5          )                          (          x          +          3          )                      ≥    0        ⇒                            x          2                -        2        x        -        13                              (          x          +          5          )                          (          x          +          3          )                      ≥    0        ⇒                            (          x          -          1          -                                    14                                )                          (          x          -          1          +                                    14                                )                                      (          x          +          5          )                          (          x          +          3          )                      ≥    0  We have following zeros in order of magnitude :      ...    .    -    5    ...    .    -    3    ...    .    1    -                  14              ...    .1    +                  14              ...    .    .        -    -    -    -    -    -    -    -    -    -    -    0    +    +    +        -    -    -    -    -    -    -    0    +    +    +    +    +    +    +        -    -    -    -    -    0    +    +    +    +    +    +    +    +    +        -    -    0    +    +    +    +    +    +    +    +    +    +    +    +              =========================            +    +    0    -    -    -    0    +    +    0    -    -    -    0    +    +    +              We see               ≥    0                 occurs for               x    &amp;lt;    -    5                 and               x    ≥    1    +                  14                           and             -    3    &amp;lt;    x    ≤    1    -                  14                    .

What are the boundaries of x if <mstyle displaystyle="true"> 2 x

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