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Question 621559: i have tried this so many times.....
3x+9<4(x-5)-x+3+2x
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there--
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Solve for x. It looks messy, but we'll go through it step by step.
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Clear the parentheses on the right side of the inequality.
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Start on the right and begin by combining x-terms, 4x-x+2x is 5x.
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We want all the x-terms on the left so we subtract 5x from both sides.
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Combine the x-terms again, 3x-5x is -2x, and 5x-5x=0.
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We want all the constant terms on the right side of the inequality, so we subtract 9 from both sides of the equation.
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Simplify both sides of the inequality, 9-9 is 0 and -17-9 is -26.
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We want x by itself on the left side of the inequality, so we divide both sides by -2. IMPORTANT NOTE: when you divide both sides of an inequality by a negative number, the direction of the inequality will change ("less than" becomes "greater than.")
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Simplify one last time. -2x/-2 is just x, and -26/-2 is 13.
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A good way to check your work (always a good idea) is to substitute 13 for x in the original inequality. If your answer is correct, both sides will simplify to the same value.
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On the left side, we have 39+9=48. On the right side, we have 52-20-13+3+26=48. Good.
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We also want to check that we got the inequality sign in the right direction. All our algebra shows that x>13. Choose any value for x that is greater than 13, say 15. Substitute 15 in the original equation. When you simplify, you should get a true statement.
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This is true, so we know that we have the inequality sign in the correct direction. The solution to this rather long, messy inequality is x>13.
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Hope this helps! This was a long explanation. Please do email me if there is any part that does not make sense yet.
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Ms.Figgy
math.in.the.vortex@gmail.com
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