check my absolute value answers asap please

Question

         | = absolute value

 

1. question =   |3x-5| = 7                                 My answer =          x= 2/3

 

 

2. question =  -2|4x-1|+7 = -3                          My answer =          x= 1

 

 

3. question =  3|x²-3x-1| -3 = 3                        My answer =           x = -3 + √13 over 2

 

Please check and correct where necessary!     

Answer 1

Josh, none of the answers are correct. You can actually check it by substituting your answers back into the equation.

 

For example, let's check if x=2/3 is one of the solutions of |3x-5| = 7

|3(2/3) - 5| = 7

|2 - 5| = 7

|-3| = 7

3 = 7

Which is not correct. So, x=2/3 is not one of the solutions of |3x-5| = 7

 

You can also check your answers in 2 and 3 by plugging them back into the equations.

 

So what's the correct answer? Let's do problem 1

 

|3x-5| = 7

3x - 5 = 7        or       3x - 5 = -7

3x = 7+5         or       3x = -7+5

x = 12/3          or       x = -2/3

x=4                 or       x= -2/3

So there are actually two solutions: x=4 and x=-2/3

 

Second problem is similar to the first problem, so I am leaving it for you to work it out.

 

Let's look at problem 3

3|x2-3x-1| -3 = 3

|x2-3x-1| -1 = 1  (divided each side with 3)

|x2-3x-1| = 2      (added 1 on each side)

x2-3x-1 = 2          or         x2-3x-1 = -2

x2-3x-3 = 0          or         x2-3x+1 = 0

x = (3 ± √21)/2    or         x = (3 ± √5)/2

So, you have 4 solutions: x = (3 ± √21)/2  and  x = (3 ± √5)/2

 

Answer 2

O.K.  Checking . . . . .    (picture the computer slider downloading or the hour glass or the circle).

 

1.   Is       | 3*(2/3) - 5 |  = 7       ??

               | 2 - 5 | = 7

               | -3 |  = 7          NO !   try   -2/3

                                either 3x-5 = 7  or else  -(3x-5) = 7 

                    so, why don't you have two answers   (also x=4)

 

2.   Is    -2|4*(-1) -1| + 7 = -3

              -2|-5| + 7 = -3

                10 + 7  = -3

                                  SORRY!

                        again either 

                    -2*(4x-1) + 7 = -3       or -2*(-(4x-1)) = -3

                        I got x=5/2    or x=1

      Hmm, seems if you check (plug in the values), you could do this yourself; I hate grading papers!

 

3.  Is 3 |x2 -3x-1| - 3 = 3    ?

 

        It looks like you used the quadratic equation, but made a calculation error.  And, you only listed one of the answers.   Where are the others?

 

Again, it’s worth your time to check all your answers (it also makes it easy for teachers to grade, so you get A's)