Posted by vicki on Thursday, August 31, 2006 at 5:33pm.
how do you solve this problem?
1/2x - 3 = -1
Let me make sure I understand the problem. Do you mean
(1/2)x - 3 = -1, i.e. .5x-3 = -1?, or
1/(2x) - 3 = -1
I'm going to suppose you mean the first one.
There is one very simple, but very important postulate of algebra you need to understand at the beginning, otherwise algebra can seem impossible. Some don't seem to grasp this at the beginning and it causes problems later on.
That important postulate states: If we are given an equation (meaning there is an '=' sign) and as long as we perform the same operations on each side of the equation, the equality between the sides is unaffected.
Does that make sense?
Some texts usually state this observation as two postulates, an addition one and a multiplication one.
They tell you that as long as the same (or equivalent) quantities are add to each side, equality remains. Further, they'll make a similar statement for multiplication. As long as each side is multiplied by the same (or equivalent) quantities, the equality is uaaffected. These are occasionally called addition and multiplication postulates of algebra. Having said that, your question is to solve the equation
1/2x - 3 = -1
If we add 3 to both sides we have
(1/2)x = -1 + 3 = 2 so we have
(1/2)x = 2. If we now multiply both sides by 2, we have
2(1/2)x = 2*2=4 or,
2(1/2)*x = x = 4
Now test the answer. (1/2)*4-3=2-3=-1
Does this process look familiar. If not, keep practicing until working these equations becomes natural.
I was with you all the way up until the 2(1/2)*x=x=4
a typo, that's what happens when I try to mult-task and do math at the same time. I meant to hit '*'.
It should be 2(1/2)*x = 4
But as long as you follow the previous part I think you'll do fine.
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