How do you solve 4 |4-3x |= 4x + 6 and find any extraneous solutions?

2 Answers
Jun 28, 2016

x=5/8 and x=11/4

Explanation:

The equation is equivalent to:

(4-3x>=0 and 4(4-3x)=4x+6) or (4-3x<0 and 4(-4+3x)=4x+6)

that becomes:

(x<=4/3 and 16-12x=4x+6) or (x>4/3 and -16+12x=4x+6)

(x<=4/3 and 16x=10) or (x>4/3 and 8x=22)

(x<=4/3 and x=5/8) or (x>4/3 and x=11/4)

so

x=5/8 and x=11/4

Jun 28, 2016

x=5/6 and 11/4. There is no extraneous solution.

Explanation:

Divide by 4 and make it

|4-3x|=x+3/2>=0 So, the solution(s) should satisfy x>=-3/2.

The given equation is equivalent to the pair

4-3x=x+1.5, when x<=4/3.and

3x-4=x+1.5, when x>=4/3.

Solving both,

x=5/8<4/3 and x=11/4>4/3.

Both are valid..

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