To prove that [tex]\mathbf{x = \frac{62}{9}}[/tex] given that [tex]9(x+6)-41=75[/tex], the following are the missing statements and reasons for the stated proof:
Statement 1: [tex]9(x+6) - 41=75[/tex]
Reason: Given
Statement 2: [tex]9(x+6) = 116[/tex]
Reason: Addition Property of Equality
Statement 3: [tex]9x + 54 = 116[/tex]
Reason: Distributive Property
Statement 4: [tex]9x = 62[/tex]
Reason: Subtraction Property of Equality
Statement 5: [tex]x = \frac{54}{6}[/tex]
Reason: Division Property of Equality
Given the algebraic equation, 9(x+6) − 41 = 75, to prove that x = 62/9, we would solve the equation using several properties as shown below:
Statement 1: [tex]9(x+6) - 41=75[/tex]
Reason: Given (You first of all state what is given)
Statement 2: [tex]9(x+6) = 116[/tex]
Reason: Addition Property of Equality
This is arrived at as shown below:
[tex]9(x+6) - 41 + 41 =75 + 41\\\\9(x+6) = 116[/tex]
Statement 3: [tex]9x + 54 = 116[/tex]
Reason: Distributive Property
This is arrived at as shown below:
[tex]9 \times x + 9 \times 6 = 116\\\\9x + 54 = 116[/tex]
Statement 4: [tex]9x = 62[/tex]
Reason: Subtraction Property of Equality
This is arrived at as shown below:
[tex]9x + 54 - 54 = 116 - 54\\\\9x = 62[/tex]
Statement 5: [tex]x = \frac{54}{6}[/tex]
Reason: Division Property of Equality
This is arrived at as shown below:
[tex]9x = 62\\\\\mathbf{x = \frac{62}{9}}[/tex]
In summary, to prove that [tex]\mathbf{x = \frac{62}{9}}[/tex] given that [tex]9(x+6)-41=75[/tex], the following are the missing statements and reasons for the stated proof:
Statement 1: [tex]9(x+6) - 41=75[/tex]
Reason: Given
Statement 2: [tex]9(x+6) = 116[/tex]
Reason: Addition Property of Equality
Statement 3: [tex]9x + 54 = 116[/tex]
Reason: Distributive Property
Statement 4: [tex]9x = 62[/tex]
Reason: Subtraction Property of Equality
Statement 5: [tex]x = \frac{54}{6}[/tex]
Reason: Division Property of Equality
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