Question 614778: How to work out equation 4(m-3)=m+6 ?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The general idea of solving linear equations such as this one is to do what is necessary to get the unknown variable on the left side of the equal sign and the numbers on the right side. Looking at the problem you are given should tell you that you have to do a little work to do that.
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First, note that on the left side you have a distributed multiplication, so you need to multiply that out. Do this multiplication by multiplying the 4 times each of the terms in the parentheses. 4 times m is 4m and 4 times -3 is -12. So after the multiplication, the equation becomes:
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4m - 12 = m + 6
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Now we are ready to collect all the terms containing m on the left side of the equal sign and all the numbers on the right side. Remember that whatever we do to one side of an equation we must also do to the other side to keep the equality unchanged.
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Let's get rid of the m on the right side by subtracting m on the right side. But if we do that we must also subtract an m from the left side. This subtraction results in:
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4m - m - 12 = m - m + 6
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On the left side the 4m - m results in 3m and on the right side the m - m results in zero, meaning that the m is gone on the right side. So our equation is then:
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3m - 12 = 6
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Now let's get rid of the -12 on the left side. We can do that by adding +12 to the left side, but then we must also add +12 to the right side:
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3m - 12 + 12 = 6 + 12
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On the left side the -12 and the + 12 add to zero, so the -12 has disappeared from the left side. On the right side the 6 + 12 adds to 18. What's left is:
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3m = 18
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Finally, our goal is to solve for m. On the left side we have 3m and we can make that just m if we divide the left side by 3. But to do that we must also divide the right side by 3. This is shown as follows:
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3m/3 = 18/3
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And when we do these divisions we get the answer:
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m = 6
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That's the answer to the problem. We can check it by returning to the original problem and substituting 6 for m as follows:
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4(m - 3) = m + 6
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Now let m be 6:
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4(6 - 3) = 6 + 6
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Do the subtraction in the parentheses of 6 - 3 which gives 3:
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4(3) = 6 + 6
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Multiply out the left side (4 times 3 is 12) and do the addition on the right side ( 6 + 6 = 12). This results in:
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12 = 12
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And since the left side and right side are both 12 when m is 6, we know we have solved the problem correctly.
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When m equals 6 the equation is equal on both sides.
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Hope this helps you to have a little better understanding of what can be done to solve equations such as this.
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