Answered

Agustin solved an equation as shown. What error did Agustin make? What is the correct answer?

1/3x - 4 = 3/4x + 1

12 (1/3x) - 4 = 12(3/4x) + 1

4x - 4 =9x + 1

-5 = 5x

x= -1

Verified Answer :

(1/3x)-3/4x=1+5
(4 1-3  3)/12x=1+4
-5/12x=5
12x=-5/5=1
x= -1/12

The error is in the second step.

This is because when you want to remove denominators you multiply by the least common multiple of them and you multiply all the equation, not only some terms of it:

\(12(\frac{1}{3} x - 4) = 12 (\frac{3}{4}x+ 1)\)

And we can continue solving:

\(4x - 48 = 9x + 12 \\5x=-60\\x=\frac{-60}{5} = -12\)

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