SOLUTION: 3x*16=12*4

SOLUTION: 3x16=124

Question 559930: 3x*16=12*4
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You are asked to solve for x given the equation:
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3x*16=12*4
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Before we begin, let's remember that 3x means 3 times x. So x is being multiplied by 3. With that in mind we can think of 3x as being written as 3*x to show the multiplication. So really the left side of the equation can be written as shown below:
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3*x*16 = 12*4
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Think about this: In a series of multiplications we can arrange the terms in any order as long as we end up multiplying all the terms. For example, if you were given a multiplication problem such as 4*6*5*2 you could multiply it in the order given or in other orders such as 5*4*2*6 or maybe 2*4*5*6 or 5*6*2*4. It doesn't make any difference in what order you do this multiplication you will always get 240 as an answer.
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Now let's get back to your problem. The left side of the equation is 3*x*16. We can rearrange the terms to 16*3*x and then multiply the 16 times 3 first. 16 times 3 is 48. Then we multiply the 48 times x and get 48x. So with this form the equation has become:
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48x = 12*4
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Now on the right side multiply the 12*4 to get 48 and this makes the equation:
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48x = 48
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Finally, divide both sides of this equation by the number multiplying the x. That number is 48. When you divide 48x by 48 the answer is just x. So the left side of the equation is now just x. But don't forget ... since you divided the left side by 48 you must also divide the right side by 48. 48 divided by 48 is just 1. So we have reduced the equation to be:
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x = 1
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and that's the answer.
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We can check this answer by returning to the original problem and replacing x by 1 to see if the left side of the equation equals the right side. If it does, then our answer for x is correct.
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The original problem was:
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3x*16=12*4
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We replace x by 1 and the original problem becomes:
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3*1*16 = 12*4
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When you multiply 3 times 1 times 16 you get 48. And on the right side of the equation when you multiply 12 times 4 you get 48. So with x = 1, the equation simplifies to:
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48 = 48
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Our answer checks. If x were something other than 1, the left side would not have equaled the right side so we would know that this was a wrong value for x.
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I hope this explanation helps you to understand a little more about algebraic equations.
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