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Question 502725: -2(x+4)>6x-4
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! -2(x+4)>6x-4
Multiply -2 by each term inside the parentheses (x+4).
(-2(x)-2(4))>6x-4
Multiply -2 by the x inside the parentheses.
(-2*x-2(4))>6x-4
Multiply -2 by x to get -2x.
(-2x-2(4))>6x-4
Multiply -2 by the 4 inside the parentheses.
(-2x-2*4)>6x-4
Multiply -2 by 4 to get -8.
(-2x-8)>6x-4
Remove the parentheses around the expression -2x-8.
-2x-8>6x-4
Since 6x contains the variable to solve for, move it to the left-hand side of the inequality by subtracting 6x from both sides.
-2x-8-6x>-4
According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, x is a factor of both -2x and -6x.
(-2-6)x-8>-4
Subtract 6 from -2 to get -8.
(-8)x-8>-4
Remove the parentheses.
-8x-8>-4
Since -8 does not contain the variable to solve for, move it to the right-hand side of the inequality by adding 8 to both sides.
-8x>8-4
Subtract 4 from 8 to get 4.
-8x>4
Divide each term in the inequality by -8.
-(8x)/(-8)<(4)/(-8)
Move the minus sign from the denominator to the front of the expression.
-(-(8x)/(8))<(4)/(-8)
Cancel the common factor of 8 in -(8x)/(8).
-(-(8x)/(8))<(4)/(-8)
Remove the common factors that were cancelled out.
-(-x)<(4)/(-8)
Multiply -1 by the -x inside the parentheses.
x<(4)/(-8)
Move the minus sign from the denominator to the front of the expression.
x<-((4)/(8))
Cancel the common factor of 4 in (4)/(8).
x<-((4)/(28))
Remove the common factors that were cancelled out.
x<-((1)/(2))
Multiply -1 by the (1)/(2) inside the parentheses.
x<-(1)/(2)
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