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Algebra 1 - Solve for Unknown













































Use the PEMDAS order of operations to simplify the following equation, combine like terms, and then solve for the unknown.

8m - (8 - m) = 28

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Sep 05, 2011
Equation - Solve for Unknown
by: Staff


The question:


8m - (8 - m) = 28


The answer:

Simplify each side of the equation to the maximum extent:

8m - (8 - m) = 28


1. You should use the PEMDAS order of operations for the simplification process.

PEMDAS order tells you what to do first, second, . . . etc.

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction


Step 1: you should evaluate the expression inside each set of PARENTHESES

PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

There is one expression enclosed in parentheses:

(8 - m)

This expression (inside the parentheses) cannot be simplified further. For the moment, it will remain (8 - m)



Step 2: evaluate EXPONENTS


PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

There are no exponents to evaluate.


Step 3: MULTIPLICATION


PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

8m - (8 - m) = 28

There is one place where you should complete the multiplication now:

- (8 - m)

= (-1) * (8 - m)

= (-1) * (8) + (-1) * (-m)

= -8 + m


After completing the multiplication, the equation should look like this:


8m - 8 + m = 28


Step 4: DIVISION


PEMDAS order of evaluation: parentheses, exponents, multiplication, DIVISION, addition, subtraction

No division is necessary to simplify either side of the equation. However, you will use division to solve for the final value of m.

Step 5: evaluate ADDITION & SUBTRACTION

PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

You can combine like terms on the left side of the equation now:

8m - 8 + m = 28

8m + m - 8 = 28

9m - 8 = 28



At this point, you have used the PEMDAS order of operations to simplify the expression on each side of the equation to the maximum extent possible.


2. You can now solve for the final value of m.

To eliminate the -8 from the left side of the equation, add 8 to each side of the equation:

9m - 8 + 8 = 28 + 8

9m + 0 = 28 + 8

9m = 28 + 8

9m = 36

To eliminate the 9 from the left side of the equation, divide each side of the equation by 9:

9m = 36

9m/9 = 36/9

m*(9/9) = 36/9

m*(1) = 36/9

m = 36/9

m = 4


the final answer is: m = 4



check the solution by substituting the numerical value of m into the original equation


for m = 4


8m - (8 - m) = 28

8 * 4 - (8 - 4) = 28

32 - (8 - 4) = 28

32 - (4) = 28

32 - 4 = 28

28 = 28, OK → m = 4 is a valid solution



Thanks for writing.

Staff
www.solving-math-problems.com


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