Week 2_Concept Check

Week 2_Concept Check - 7x – 17 = 4 + 7(x-3) 7x – 17 = 4...

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Week 2 Concept Check Post your 50-word response to the following: How do you know when an equation has infinitely many solutions? How do you know when an equation has no solution? How do you know when an equation has infinitely many solutions? Consider: 3 + x = x + 3 We know by the commutative law of addition that this equation holds for any replacement of x with a real number. 3 + x = x + 3 -x + 3 + x = -x + x + 3 3 = 3 We end with a true equation. The original equation holds for all real-number replacements. Every real number is a solution. Thus the number of solutions is infinite. Using the distributive law to multiply and remove parentheses
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Unformatted text preview: 7x – 17 = 4 + 7(x-3) 7x – 17 = 4 + 7x – 21 7x – 17 = 7x – 17-7x + 7x – 17 = -7x + 7x – 17-17 = -17 Every real number is a solution. There are infinitely many solutions. How do you know when an equation has no solution? Consider: 3 + x = x + 8 3 + x = x + 8-x + 3 + x = -x + x + 8 3 = 8 We end with a false equation. The original equation is false for all real number replacements. Thus it has no solutions. Using the distributive law to multiply and remove parentheses 3x + 4(x + 2) = 11 + 7x 3x + 4x + 8 = 11 + 7x 7x + 8 = 11 + 7x 7x + 8 – 7x = 11 + 7x – 7x 8 = 11...
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This note was uploaded on 06/26/2011 for the course MAT 116 taught by Professor Universityofphoenix during the Spring '09 term at University of Phoenix.

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