Transcript ALGEBRA REVIEW

MAT111
ALGEBRA REVIEW
Three Basic Rules
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MAT111
Three Basic Rules
• Add or subtract the same quantity on both
sides of the equation
• Multiply or divide both sides of the
equation by the same quantity (as long as
that quantity is not zero)
• Interchange the left and right sides of an
equation
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MAT111
Three Basic Rules (cont.)
What good are the three basic rules?
To help solve equations that involve
unknowns!
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MAT111
Adding and Subtracting Examples
Problem: Solve the equation x  8 = 4 for x
Solution: Isolate x by adding 8 to both sides
x  8  8 = 4  8  x = 12
Problem: Solve the equation y  5 = 2y for y
Solution: Isolate y by subtracting y from both sides
y  5  y = 2y  y  5 = y
(interchanging both sides)  y = 5
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MAT111
More Examples
• What if there is more than one unknown?
Problem: Solve 7q – 16 = p + 4q – 2 for p
Solution: Isolate p by subtracting 4q from both sides
and adding 2 to both sides
7q – 16 – 4q + 2 = p + 4q – 4q – 2 + 2  3q – 14 = p

(interchanging both sides)  p = 3q – 14
Note: We cannot state a numerical value for p until we know the value of q
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MAT111
Multiplying and Dividing Examples
Problem: Solve the equation 5x = 25 for x
Solution: Isolate x by dividing both sides by 5
5 x 25

 x5
5
5
3
z
Problem: Solve the equation
 2  10 for z
4
Solution: Isolate z by adding 2 to both sides, then
multiply both sides by 4/3
3z
3z
3z 4
4
 2  2  10  2 
 12 
  12   z  16
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4
4 3
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