SOLUTION: Solve for x, then graph and express the solution in interval notation. -2(1-x)-(3x+1)>=4x-(1+x)

Algebra ->  Inequalities -> SOLUTION: Solve for x, then graph and express the solution in interval notation. -2(1-x)-(3x+1)>=4x-(1+x)       Log On


   

Question 974387: Solve for x, then graph and express
the solution in interval notation.
-2(1-x)-(3x+1)>=4x-(1+x)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-2%281-x%29-%283x%2B1%29%3E=4x-%281%2Bx%29

-2%2B2x-3x-1%3E=4x-1-x

-x-3%3E=3x-1

-x-3%2Bx%3E=3x-1%2Bx

-3%3E=4x-1

-3%2B1%3E=4x-1%2B1

-2%3E=4x

4x+%3C=+-2

4x%2F4+%3C=+-2%2F4

x+%3C=+-1%2F2


Graph on a number line:



There is a closed circle at -1%2F2=-0.5 on the number line. The shading is done to the left of -1%2F2=-0.5

x+%3C=+-1%2F2 in interval notation is \left(-\infty, -\frac{1}{2}\right] (notice how I used a parenthesis near the negative infinity, and a square bracket near the -1/2)

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