Determine which of the following equations have the same solution set by recognizing properties rather than solving.
a. 2x + 3 = 13 - 5x
b. 6 + 4x = 10x + 26
c. 6x + 9 = 13/5 - x
d. 0.6 + 0.4x = x + 2.6
e. 3(2x + 3) = 13/5 -x
f. 4x = -10x + 20
g. 15(2x + 3) = 13 - 5x
h. 15(2x + 3) + 97 = 110 - 5x

Respuesta :

Answer

a) 2 x + 3 = 13 - 5 x

   7 x = 13 -3

   7 x = 10

      [tex]x = \dfrac{10}{7}[/tex]

b) 6 + 4 x = 10 x + 26

     6 x = 20

        [tex]x = \dfrac{20}{6}[/tex]

        [tex]x = \dfrac{10}{3}[/tex]

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

    [tex]7 x = \dfrac{13}{5} -9[/tex]

       [tex]x = \dfrac{-32}{35}[/tex]

d) 0.6 + 0.4 x = x + 2.6

         0.6 x = -2

        [tex]x = \dfrac{-20}{6}[/tex]

        [tex]x = \dfrac{-10}{3}[/tex]

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

   6 x + 9 = 13/5 - x

    [tex]7 x = \dfrac{13}{5} -9[/tex]

       [tex]x = \dfrac{-32}{35}[/tex]

f) 4 x = -10 x + 20

      14 x = 20

          [tex]x = \dfrac{20}{14}[/tex]

          [tex]x = \dfrac{10}{7}[/tex]

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

    30 x + 45 = 13 - 5 x

         35 x = -32

       [tex]x = \dfrac{-32}{35}[/tex]

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

   30 x + 45 + 97 = 110 - 5x

    35 x = -32

   [tex]x = \dfrac{-32}{35}[/tex]

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

      the solution of part a, f  is same which is [tex]x = \dfrac{10}{7}[/tex]