Question 606120: How do I solve: r-(-7)= -1-6? I can't remember the steps to solve this. Any help is appreciated. Thank you.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given to solve:
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r - (-7) = - 1 - 6
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Before we start, let's talk about the general strategy for solving this equation. Our overall goal will be to get the unknown number r on one side of the equal sign and get a number on the other. Usually, but not always, we'll get the r on the left side and the number on the right side. An example of the solution might be r = 10.
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Now lets work toward that goal. You can see that we already have r on the left side. So we need to do a couple of things. First, there is a number on the left side, and we'll need to remove that from the left side by moving it to the right side. When we do that we'll have several numbers on the right side and we'll need to combine them into a single number.
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So let's start with the given problem and let's see what we can do with it.
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r - (-7) = - 1 - 6
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Here's a rule to remember. If you have a set of parentheses preceded by a + sign you can remove the + sign and the parentheses without changing the signs of the terms in the parentheses. But if you have a set of parentheses preceded by a - sign, you can remove that - sign and the parentheses, but in doing so you need to change the signs of all the terms in the parentheses.
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Notice on the left side we have a set of parentheses preceded by a minus sign. We can erase that - sign and the parentheses, but we need to change the sign of the -7 that is inside the parentheses. So we take out the - sign in front of the parentheses, and also take out the two parentheses symbols ( and ), but in doing so we change the -7 to a +7. After that, the equation becomes:
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r + 7 = - 1 - 6
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Now let's move the + 7 on the left side to the right side. We do this by subtracting 7 from the left side. But the rules of equations say that whatever you do to one side of an equation, you must also do to the other side. Therefore, since we are going to subtract 7 from the left side, we must also subtract 7 from the right side. This will make our equation look like this:
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r + 7 - 7 = - 1 - 6 - 7
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On the left side the + 7 and the - 7 cancel each other out and the left side becomes just r as shown below:
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r = - 1 - 6 - 7
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Now all we have to do is to combine the three numbers on the right side. The - 1 and the - 6 combine to give - 7 as shown:
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r = - 7 - 7
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Finally, we combine the - 7 and the - 7 to get - 14 and we have solved the equation for r as:
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r = -14
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How can we check this work? We do it by going back to the original problem, substituting -14 for r, and determining if the left side equals the right side. So in checking we start with:
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r - (-7) = - 1 - 6
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We replace r with -14 to get:
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-14 - (-7) = -1 - 6
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Then we remove the - sign and the parentheses (while changing the -7 to a +7 to get:
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-14 + 7 = -1 - 6
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The -14 and the +7 combine to -7 so the equation becomes:
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-7 = -1 - 6
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And on the right side the -1 and the -6 combine to -7 so we have:
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-7 = -7
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Since both sides are equal, and we got there by setting r = -14, then we know that when r equals -14 the equation works. Therefore, we know the answer is correct.
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The answer to this problem is r = -14
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I hope this helps you to understand how to work problems such as this one.
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