Answer:
x = 8
Explanation:
1. Group all x terms on the left side of the equation
1/3· x+4=-2/3·x+12
Add 2/3x to both sides:
1/3x+4+2/3·x=-2/3x+12+2/3·x
Group like terms:
1/3·x+2/3·x+4=-2/3·x+12+2/3·x
Combine the fractions:
1+2/3·x+4=-2/3·x+12+2/3·x
Combine the numerators:
3/3·x+4=-2/3·x+12+2/3·x
Find the greatest common factor of the numerator and denominator:
1·3/1·3·x+4=-2/3·x+12+2/3·x
Factor out and cancel the greatest common factor:
1x+4=-2/3·x+12+2/3·x
Simplify the left side:
x+4=-2/3·x+12+2/3·x
Group like terms:
x+4=-2/3·x+2/3·x+12
Combine the fractions:
x+4=-2+2/3·x+12
Combine the numerators:
x+4=0/3·x+12
Reduce the zero numerator:
x+4=0x+12
Simplify the arithmetic:
x+4=12
2. Group all constants on the right side of the equation
Subtract 4 from both sides:
x+4-4=12-4
Simplify the arithmetic:
x=12-4
Simplify the arithmetic:
x=8