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Question 956852: Make the following equation true by inserting 1 or more parentheses. Show all your steps to prove your answer.
-12+2*-1^2+-3^2-9/2=-7
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is:
-12 + 2 * -1^2 + -3^2 -9 / 2=-7
you would need to insert parentheses as shown below:
(-12 + 2 * -1^2 + (-3)^2 - 9) / 2 = -7
the parentheses around the (-3) indicates that you are squaring (-3) rather than 3.
the parentheses around (-12 + 2 * -1^2 + (-3)^2 - 9) means that whole expression has to be evaluated before you divide by 2.
there is no parentheses around -1^2.
this means that (1) will be squared first and then the minus sign applied.
-1^2 = -1
the equation, with the parentheses as shown, would be processed as follows:
start with:
(-12 + 2 * -1^2 + (-3)^2 - 9) / 2 = -7
you process exponents first, working from left to right.
-1^2 becomes -1
(-3)^2 becomes 9
your equation becomes:
(-12 + 2 * -1 + 9 - 9) / 2 = -7
you are processing multiplication and division within the set of parentheses next, working from left to right.
2 * -1 = -2
since you are still working within the set of parentheses, the division by 2 is not performed until after all the operations within the set of parentheses have been completed.
your equation becomes:
(-12 - 2 + 9 - 9) / 2 = -7
you are processing addition and subtraction within the set of parentheses next.
-12 - 2 = -14
-14 + 9 = -5
-5 - 9 = -14
your expression becomes:
(-14)/2 = -7
you have finished evaluating the expression within the set of parentheses so you work on the rest of the expression next.
(-14)/2 is equal to -7
your equation becomes:
-7 = -7
you are done.
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