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Inverse of a Sum and Simplifying. Goal: To find the inverse of a sum. Review. What is an inverse of a #?? The opposite sign 4 , -4 or -6, 6 What is the notation of an inverse?? -(x) The notation for inverse of a sum is –(a+b). Inverse of a Sum. -(3x +5 – 8c) - 1 (3x+5 +- 8c)
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Inverse of a Sum and Simplifying Goal: To find the inverse of a sum
Review • What is an inverse of a #?? The opposite sign 4 , -4 or -6, 6 • What is the notation of an inverse?? -(x) • The notation for inverse of a sum is –(a+b)
Inverse of a Sum -(3x +5 – 8c) -1 (3x+5+-8c) -1(3x)+-1(5) +-1(-8c) -3x +-5 +8c
Steps • Change all subtraction to addition of the inverse • If there is not a number in front of the parenthesis put an imaginary 1 there • Distribute • Collect like terms
Inverse of a Sum Property For any rational numbers a and b, -(a + b) = -a + (-b) We sometimes say, “we change the sign of every term”
Rewrite the expression without parenthesis: - (x + 2) -x + (-2) -x - 2
Rewrite the expression without parenthesis: - (a - 7) -a + 7
Rewrite the expression without parenthesis: - (5x + 2y - 8) -5x – 2y + 8
Rewrite the expression without parenthesis: - (3c – 4d + 1) -3c + 4d -1
11n-(3n-7) 11n – (3n-7) 11n +-1(3n +-7) 11n +-1(3n) +-1 (-7) 11n +-3n +7 8n +7
Simplify: 3x – (6x + 2) 3x+ -1 (6x +2) 3x +- 6x +-2 -3x -2
Simplify: 3 – (x + 1) 3 +-1 (x+1) 3 +- x +- 1 2 +- x
Simplify: 3z – 2y – (4z + 5y) 3z+- 2y+- 4z +-5y -1z + -7 y
Simplify: 7k – 3(7k + t) 7k + -3 (7k + t) 7k – 21k – 3t -14k – 3t
2x +7x –(4x +6) 9x +-1 (4x +6) 9x +-1(4x) +-1(6) 9x +-4x +-6 5x +-6