Solve each absolute value Equation.

Question

5f -|3f + 4|=20 

Answer 1

If B > 0 and l A l = B, then A = ±B.

 

Rearrange the terms to get l 3f+4 l = 5f - 20

 

Then, 3f + 4 = 5f - 20 or 3f + 4 = -(5f - 20)

 

So, -2f = -24 or 8f = 16

 

Therefore, f = 12 or f = 2

 

2 does not satisfy the given equation, but 12 does.  So, the only solution is 12.  

 

Note:  l 3f + 4 l = 5f - 20.  Since l 3f + 4 l ≥ 0, 5f - 20 can't be negative.  so 5f ≥ 20.  Thus, f ≥ 4.  So, f = 2 is not possible.   

Answer 2

If the value "f" = -3, then your equation is...

 

-15-[-3*3+4]=20

=15+[-9+4]=20

=15+[-5]=20

=15+5+20, therefore "f" is -3.