Question 257516: Raising rabbits. Before Roland sold two female rabbits, half of his rabbits were female. After the sale, only one third of his rabbits were female. If x represents his original number of rabbits, then
1/2x-2=1/3(x-2)
Solve this equation to find the number of rabbits that he had before the sale.
Answer by jmorgan22(8)   (Show Source):
You can put this solution on YOUR website! 1/2x-2=1/3(x-2)
Multiply 1/2by x to get x/2
x/2-2=1/3(x-2)
Multiply the rational expressions to get (x-2/3
x/2-2=x-2/3
Multiply each term in the equation by 3.
x/2*3-2=x-2/3*3
Simplify the left-hand side of the equation by canceling the
common factors.
3x/2-6=x-2/3*3
Simplify the right-hand side of the equation by simplifying each term.
3x/2-6=x-2
Since x contains the variable to solve for, move it to the left-hand side of the equation by subtracting x from both sides.
3x/2-6-x=-2
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 2. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-x*2/2+3x/2-6=-2
Complete the multiplication to produce a denominator of 2 in each expression.
-2x/2+3x/2-(6)=-2
Combine the numerators of all expressions that have common denominators.
-2x+3x/2-(6)=-2
Combine all like terms in the numerator.
x/2-6=-2
Since -6 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 6 to both sides.
x/2=6-2
Subtract 2 from 6 to get 4.
x/2=4
Multiply each term in the equation by 2.
x/2*2=4*2
Simplify the left-hand side of the equation by canceling the common factors.
x=4 • 2
x=4*2
Multiply 4 by 2 to get 8.
x=8
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