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Question 346803: 1/2y + 2 >= 1/3y - 4
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (1)/(2)*y+2>=(1)/(3)*y-4
Multiply (1)/(2) by y to get (y)/(2).
(y)/(2)+2>=(1)/(3)*y-4
Multiply (1)/(3) by y to get (y)/(3).
(y)/(2)+2>=(y)/(3)-4
Since (y)/(3) contains the variable to solve for, move it to the left-hand side of the inequality by subtracting (y)/(3) from both sides.
(y)/(2)+2-(y)/(3)>=-4
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 6. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-(y)/(3)*(2)/(2)+(y)/(2)*(3)/(3)+2>=-4
Complete the multiplication to produce a denominator of 6 in each expression.
-(2y)/(6)+(3y)/(6)+2>=-4
Combine the numerators of all expressions that have common denominators.
(-2y+3y)/(6)+2>=-4
Combine all like terms in the numerator.
(y)/(6)+2>=-4
Since 2 does not contain the variable to solve for, move it to the right-hand side of the inequality by subtracting 2 from both sides.
(y)/(6)>=-2-4
Subtract 4 from -2 to get -6.
(y)/(6)>=-6
Multiply each term in the inequality by 6.
(y)/(6)*6>=-6*6
Simplify the left-hand side of the inequality by canceling the common factors.
y>=-6*6
Multiply -6 by 6 to get -36.
y>=-36
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