Solving Basic Equations with VariablesDate: 11/28/2004 at 12:05:05 From: Liz Subject: I don't understand this question and I have a test soon. How do I solve an equation like 8x + 6 = 3x + 21? I don't know how to start it. Date: 11/29/2004 at 08:43:35 From: Doctor Boyd Subject: Re: I don't understand this question and I have a test soon. Hi Liz, Thanks for writing in to Dr. Math. Let's look at a similar question: 3x + 1 = 2x + 4 We could think about this graphically, with a rectangle being an x and a square being a 1: _____ _____ _____ _ _____ _____ _ _ _ _ |_____| |_____| |_____| |_| = |_____| |_____| |_| |_| |_| |_| The equal sign means that the left side is balanced by the right side. Just like on a balance scale, if I take the same amount away from each side (or add the same amount to each side) the scale will stay balanced. So I notice I can take away two of the x's from each side, which leaves me with: _____ _ _ _ _ _ |_____| |_| = |_| |_| |_| |_| Also, I can take one of the 1's away from each side: _____ _ _ _ |_____| = |_| |_| |_| So x = 3. This can also be done with algebra: 3x + 1 = 2x + 4 3x + 1 - 2x = 2x + 4 - 2x -->(Subtract 2x from each side) 3x - 2x + 1 = 2x - 2x + 4 -->(Collect like terms) 1x + 1 = 4 -->(Simplify) 1x + 1 - 1 = 4 - 1 -->(Subtract 1 from each side) 1x = 3 -->(Simplify) x = 3 Has this helped you with your question? Please write back if you'd like some more help with this, or if you have any other questions. All the best, - Doctor Boyd, The Math Forum http://mathforum.org/dr.math/ |
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