Simplifying ExpressionsDate: 11/24/97 at 02:23:53 From: Jacques Thurman Subject: Regarding Simplifying Expressions Hello Dr. Math, My name is Lisa Pagan and I am in 9th Grade. I am stuck on lots of problems but I really need your help on this one particular problem: 2x - ( 3 - x ) = x - 7 Date: 11/24/97 at 16:07:31 From: Doctor Bruce Subject: Re: Regarding Simplifying Expressions Hello Lisa, I would guess that you want to "solve" this equation for x. That means you would like to find a number to substitute for x which will make the equation true. It helps to understand that all the fancy symbols we use in algebra are just different names for numbers. We can add and subtract with "x" because we can add and subtract with numbers, and "x" is going to turn out to be some number. Here's what we do. First, we apply the Distributive Law to the parentheses. The negative sign has to be distributed over both the 3 and the -x which are inside the parentheses. After we do that, the equation looks like 2x - 3 + x = x - 7 We see that there is an x term on both sides of the equation, so we can subtract x from both sides (remember, x is just a number!) to get 2x - 3 = - 7 The strategy, you see, is to isolate the x term by itself on the left side of the equation. Let's add 3 to both sides now - this will get rid of the -3 on the left side. Now we have 2x = -4. We're pretty close now. We know that twice the number x equals -4, so let's divide both sides of the equation by 2. Then we have x = -2. It looks like the answer we wanted is x = -2. What you should do now is go back to the original equation and substitute the value -2 for x to see that you get a true statement. You should get the value -9 for both sides of the equation. Since -9 = -9 is a true statement, you have checked that your answer x = -2 is correct. Good luck with your future equations, -Doctor Bruce, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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