Question

Determine which of the following equations have the same solution set by recognizing properties rather than solving.

Answer 1

Answer

a) 2 x + 3 = 13 - 5 x

   7 x = 13 -3

   7 x = 10

      $x = \dfrac{10}{7}$

b) 6 + 4 x = 10 x + 26

     6 x = 20

        $x = \dfrac{20}{6}$

        $x = \dfrac{10}{3}$

c) 6 x + 9 = 13/5 - x

    $7 x = \dfrac{13}{5} -9$

       $x = \dfrac{-32}{35}$

d) 0.6 + 0.4 x = x + 2.6

         0.6 x = -2

        $x = \dfrac{-20}{6}$

        $x = \dfrac{-10}{3}$

e) 3(2x + 3) = 13/5 -x

   6 x + 9 = 13/5 - x

    $7 x = \dfrac{13}{5} -9$

       $x = \dfrac{-32}{35}$

f) 4 x = -10 x + 20

      14 x = 20

          $x = \dfrac{20}{14}$

          $x = \dfrac{10}{7}$

g) 15(2x + 3) = 13 - 5x

    30 x + 45 = 13 - 5 x

         35 x = -32

       $x = \dfrac{-32}{35}$

h)15(2x + 3) + 97 = 110 - 5x

   30 x + 45 + 97 = 110 - 5x

    35 x = -32

   $x = \dfrac{-32}{35}$

so , the solution of part c, e, g, h is same which is $x = \dfrac{-32}{35}$

      the solution of part a, f  is same which is $x = \dfrac{10}{7}$