Why do you not change the inequality sign when you are adding or subtracting?

Question

Nirdaciw3 · Accepted Answer

Step 1Consider the simplest of inequalities:             {      a      ,      b      }        ∈    ℝ  Now consider adding or subtracting a real number,       x    ∈    ℝ   to the LHS.       →    a    ±    x  The only way to restore the inequality is to add or subtract x on the RHS.Thus:       a    +    x    &amp;lt;    b    +    x                and              a    -    x    &amp;lt;    b    -    x   both follow from the original inequality. To reverse the inequality would simply be incorrect.So when must we reverse the inequality?Consider where we multiply (or divide) both sides of the inequality by       x    &amp;lt;    0   (i.e. any negative real number)As an example I will use       x    =    -    1  Then, if       a    &amp;lt;    b    ⇒    a    ×          (      -      1      )        &amp;gt;    b    ×          (      -      1      )      So, in order to maintain the inequality after multiplying or dividing through by a negative number we must reverse the inequality.

Why do you not change the inequality sign when you

Answered question

Answer & Explanation

New Questions in Pre-Algebra