Question 389671: Evaluate and graph
a. 3x+2(x+4)< 6
b. 3(x-1)-x >2x+1
c. -2x ≤10
d. -4(x+2) ≥-(2x=5)
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 3x+2(x+4)<6
Multiply 2 by each term inside the parentheses.
3x+2x+8<6
Since 3x and 2x are like terms, add 2x to 3x to get 5x.
5x+8<6
Since 8 does not contain the variable to solve for, move it to the right-hand side of the inequality by subtracting 8 from both sides.
5x<-8+6
Add 6 to -8 to get -2.
5x<-2
Divide each term in the inequality by 5.
(5x)/(5)<-(2)/(5)
Simplify the left-hand side of the inequality by canceling the common factors.
x<-(2)/(5)
3(x-1)-x>2x+1
Multiply 3 by each term inside the parentheses.
3x-3-x>2x+1
Since 3x and -x are like terms, add -x to 3x to get 2x.
2x-3>2x+1
Since 2x contains the variable to solve for, move it to the left-hand side of the inequality by subtracting 2x from both sides.
2x-3-2x>1
Since 2x and -2x are like terms, add -2x to 2x to get 0.
0-3>1
Remove the 0 from the polynomial; adding or subtracting 0 does not change the value of the expression.
-3>1
Since -3<1, there are no solutions.
No Solution
-2x<=10
Divide each term in the inequality by -2.
-(2x)/(-2)>=(10)/(-2)
Simplify the left-hand side of the inequality by canceling the common factors.
x>=(10)/(-2)
Simplify the right-hand side of the inequality by simplifying each term.
x>=-5
On the last problem, I need to make sure that is an equal sign on ≥-(2x=5),
it seems it sould be another inequality symbol.
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