Question #22412

Solve the given equation.
12a. |9x-4|=20
12b. |2x^2-x-1|=-5

Expert's answer

12a. |9x-4|=20

Consider two cases:

9x-4=20

9x=20+4=24

x = 24/9 = 8/3

or

9x-4=-20

9x=-20+4=-16

x = -16/9

So we have two solutions:

-16/9 and 8/3

-------------------------

12b. |2x^2-x-1|=-5

This equation has no solutions since the left hand sideis always non-negative:

|2x^2-x-1|>=0,

while the righthand side is negative

-5 < 0

and therefore they are nonequal for all values of x.

Consider two cases:

9x-4=20

9x=20+4=24

x = 24/9 = 8/3

or

9x-4=-20

9x=-20+4=-16

x = -16/9

So we have two solutions:

-16/9 and 8/3

-------------------------

12b. |2x^2-x-1|=-5

This equation has no solutions since the left hand sideis always non-negative:

|2x^2-x-1|>=0,

while the righthand side is negative

-5 < 0

and therefore they are nonequal for all values of x.

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