How do you solve and write the following in interval notation: x − 3 &gt; 8 and x + 2 &gt; ?

Question

How do you solve and write the following in interval notation:       x    −    3    &amp;gt;    8   and       x    +    2    &amp;gt;   ?

Carmelo Payne · Accepted Answer

Step 1Suppose the intended restrictions were                                          x            -            3            &amp;gt;            8                                                             AND                                                           x            +            2            &amp;gt;                          n                                          Since you can add or subtract the same amount to both sides of an inequality without changing the validity or direction of the inequality, these are equivalent to                                          x            &amp;gt;            11                                                             AND                                                           x            &amp;gt;                          (                              n                            -              2              )                                          Using the notation:       max          (      a      ,      b      )        =          {                                    a                                         if                                       a            ≥            b                                                b                                         if                                       a            &amp;lt;            b                              Then these restrictions can be combined into the single restriction:      x    &amp;gt;    max          (      8      ,              n            -      2      )      or in the requested interval notation:      x    ∈          (      max              (        8        ,                  n                -        2        )            ,      +      ∞      )

How do you solve and write the following in interval notation: <mstyle displaystyle="true">

Answered question

Answer & Explanation

New Questions in Pre-Algebra