SOLUTION: Not sure if this is the right page for this. Can someone help me solve this problem. I'm trying to make head and tails out of it.
5 < 2(a+1)-3(1-a)
What i'm getting is 5 < -1
Question 73856: Not sure if this is the right page for this. Can someone help me solve this problem. I'm trying to make head and tails out of it.
5 < 2(a+1)-3(1-a)
What i'm getting is 5 < -1a-1 not sure if right solution Found 2 solutions by funmath, bucky:Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website! 5 < 2(a+1)-3(1-a)
5<2a+2-3+3a
5<(2+3)a+(2-3)
5<5a-1
5+1<5a-1+1
6<5a
6/5<5a/5
:
or if you prefer the variable on the left:
Happy Calculating!!!!
You can put this solution on YOUR website! Given:
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5 < 2(a+1)-3(1-a)
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You can operate on this just as you would an equation, with a major exception that I'll discuss
later. The goal is to solve for "a" in the inequality just as you would solve for "a" if
this were and equation ... having an = sign in place of the < sign.
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Begin by doing the two distributed multiplications on the right side to get:
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5 < 2a + 2 - 3 + 3a
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Combine like terms on the right side. The 2a and the 3a add to 5a and the +2 and -3 add to -1.
Substitute these values into the inequality and you get:
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5 < 5a -1
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Now we need to get rid of the -1 on the right side. Do this by adding +1 to both sides of
the inequality:
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5 +1 < 5a -1 +1
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On the left side add the 5 and +1 to get 6 and on the right side the -1 and +1 cancel each
other out. Therefore, the inequality now becomes:
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6 < 5a
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Finally, solve for "a" by dividing both sides by 5. This gives you:
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6/5 < a
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Read this as "a" must be bigger than 6/5. You can also write the answer as:
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a > 6/5
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The "arrow" points to the smaller term.
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Let's check by letting a = 1. That is less than 6/5 so the original inequality should not
work for the value a = 1. Try it:
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5 < 2(a+1)-3(1-a) and when a = 1 this becomes
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5 < 2(1+1) - 3(1-1)
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5 < 2(2) - 3(0)
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5 < 4 ... just as you should expect. This does not work because a was less than 6/5 not
greater than.
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Let's do a similar check by letting x = 2. That is greater than 6/5 so it shoul make the
inequality work.
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5 < 2(a+1)-3(1-a) and let a = 2
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5 < 2(2+1) - 3(1 - 2)
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5 < 2(3) - 3(-1)
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5 < 6 + 1
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5 < 7
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5 is less than 7, so this time our check worked, as it was supposed to do because we
used a value of a greater than 6/5. Our answer is good.
.
Previously I mentioned that you could work inequalities just as you would an equation. There
is an exception, however. That exception is that whenever you multiply or divide both
sides of an inequality by a negative number, you must reverse the direction of the inequality.
We did not have to make use of this rule in this particular problem.
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Hope this helps you to understand inequalities a little better.
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