Knock out the false inequality claims

Exercise and reference answers

Questions

1. Question

   Three of these statements about dividing an inequality by a negative number are false.

   Choices

   1. Item

      The inequality sign reverses

      Correct

      Yes

   2. Explanation

      Only a positive divisor leaves the direction alone.

      Item

      The sign stays exactly as it was

   3. Explanation

      The solution set mirrors across zero, it does not vanish.

      Item

      The solution set becomes empty

   4. Explanation

      Nothing swaps sides, the symbol itself turns around.

      Item

      The two sides swap places instead

2. Question

   Three of these statements about checking an inequality solution are false.

   Choices

   1. Item

      Test one value in each section

      Correct

      Yes

   2. Explanation

      The solution graph splits the line into three sections.

      Item

      The graph splits into two sections

   3. Explanation

      A test is a sanity check, never a proof of the whole set.

      Item

      One passing test proves the answer

   4. Explanation

      The endpoint says nothing about the stretches on either side.

      Item

      Only the endpoint needs testing

Instructions

Tap away every false claim and leave the one true statement standing.

Explanation