Question

What is the reason for each step in the solution of the inequality? 4−3(x−5)>6x−17 select the reason for each step from the drop-down menus.

Answer 1

4 - 3(x - 5) > 6x - 17

4 - 3x + 15 > 6x - 17       distributed -3 on the left side

   -3x + 19 > 6x - 17       simplified/added like terms (4 and 15)

   -9x + 19 >      -17        subtracted 6x from both sides

    -9x       >      -36        subtracted 19 from both sides

       x       <        4          divided -9 from both sides (NOTE THE SIGN CHANGE)

Answer 2

By solving the given inequality, we get the value of "x < 4".

The given inequality is:

• $4-3(x-5)>6x-17$

By solving the bracket, we get

→  $4-3x+15 > 6x-17$

→        $19-3x> 6x-17$

By adding "17" both sides, we get

→ $19-3x+17> 6x-17+17$

→         $36-3x>6x$

By adding "3x" both sides, we get

→ $36-3x+3x>6x+3x$

→                  $36> 9x$

→                    $x > \frac{36}{9}$

→                    $x < 4$

Thus the above solution is right.

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