Ten times the sum of a number and 22 is at least 21

Question

Write the equation

Answer 1

This is not an equation; this is an inequality.

 

Let x = the number

 

"Ten times the sum of a number and 22 is at least 21"    means

Ten times  [the sum of a number and 22]  is at least 21      means

   10   *    (         x                     +   22 )    ≥     21

 

   10(x+22) ≥ 21

    10x + 220 ≥ 21              [distribute]

      10x ≥  -199                [subtract 220 from both sides retains the sense of the inequality]

        x ≥ -19.9                 [divide both sides by 10 retains the sense of the inequality]

 

Check:

  Use -20  [note:  should be false]

     Is   10(-20+22) ≥ 21   ?

           10(2) ≥ 21   >

            20 ≥ 21   ?no

 

   Use 0 [note: should be true]

      Is 10(0 + 22) ≥ 21   ?

            220 ≥ 21   ?yes