Question

2(4 – 2r) = -2(r + 5) How do you know if it's identity or no solution and show work ​

Answer 1

Answer:  r = 9

Step-by-step explanation:

2(4 - 2r) = -2(r + 5)

 8 - 4r    = -2r - 10       distributed

 8           = 2r - 10        added 4r to both sides

18           = 2r               added 10 to both sides

 9           =  r                divided both sides by 2

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Identity is when you end up with a TRUE statement after moving the x-values to one side of the equation.

For example: 2x + 2 = 2(x + 1)

                      2x + 2  = 2x + 2       distributed

                              2  =         2       subtracted 2x from both sides

                                  TRUE so x is all real numbers

No Solution is when you end up with a FALSE statement after moving the x-values to one side of the equation.

For example:  2x + 1 = 2(x + 1)

                       2x + 1 = 2x + 2       distributed

                               1 =         2       subtracted 2x from both sides

                                   FALSE so there are no solutions