CPhill

1/1,000,000 =   .000001   =   .0001 %

10%  off means she paid 90%= .90 of the cost

20% off means that she paid 80% =.80  of the cost

So we have

43(.90)  + 35(.80) = $66.70

[The dress cost $38.70  and the hangbag cost $28]

abs [5 - 11]   =   abs [ -6]    =  6

No prob, Solveit.....!!!!

f(x)  = 3x^4 − 7x^2 + 2x − 9       ......so.....

f(-x) = 3(-x)^4 - 7(-x)^2 + 2(-x)  - 9  =    3x^2 - 7x^2 - 2x  - 9

[  BTW.....This function is neither even nor odd....  ]

HUH???

5.   |x^2-x|=|x^2-1|      similar to the first one, we have

x^2 - x   = x^2 - 1                  or             x^2 - x  =  - (x^2 - 1)

-x = -1                                                   x^2 - x  = -x^2 + 1

x = 1                                                   2x^2 - x - 1  = 0

                                                           (2x +1)  ( x - 1)  = 0

                                                         Set each factor to  0

                                                            x = -1/2     [ x = 1    .....a repeated solution]

Here's the graph......https://www.desmos.com/calculator/kcbcpd3khj

4 .   |2x-7|=|x-5|

2x - 7    =    x  - 5                    or          2x - 7   = -(x - 5)

x  =  2                                                    2x - 7  = -x  + 5

                                                              3x  = 12

                                                                x = 4

Again......these are easily verified

3. |4-x|=5       this one is easy

Either

4 - x   = 5                          or                      4 - x  = -5

-x  = -1                                                         -x   = -9

x = 1                                                              x = 9

These solutions are easily verified in the original problem

2.  3|x-2|=2|x-3|    divide both sides by 2

(3/2)|x-2|=lx-3|      as before, we have.....

(3/2)(x - 2)  = x -3                and          (3/2)(x - 2)  =  -(x - 3)

                                                            (3/2)lx - 2 l  =  - x + 3

Multiply through by 2   in both equations.....

3(x -2) = 2x - 6                                     

3x - 6   = 4x - 6                                        3(x - 2)  = -2x + 6                               

The only solution to this is                     3x - 6    = -2x + 6

when x = 0  

                                                               5x  = 12

                                                                  x = 12/5  =  2 + 2/5  =  2.4

So the two solutions are  x = 0   and x  = 2.4

See the solution graphs, here.....   https://www.desmos.com/calculator/frf6guc36z