Question

Solve the given equation.

12a. |9x-4|=20

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

Answer 1

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


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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.