Naomi solved this equation:0.3(n+50)−27=0.1(n−20)0.3n+15−27=0.1n−20.3n−12=0.1n−20.2n−12=−20.2n=10n=50Which property is not needed to justify any of the steps?Choices:(A) division property of equality(B) commutative property of multiplication(C) addition property of equality(D) distributive property
Q. Naomi solved this equation:0.3(n+50)−27=0.1(n−20)0.3n+15−27=0.1n−20.3n−12=0.1n−20.2n−12=−20.2n=10n=50Which property is not needed to justify any of the steps?Choices:(A) division property of equality(B) commutative property of multiplication(C) addition property of equality(D) distributive property
Analyze equation transformation: Step 1: Analyze the equation transformation from 0.3(n+50)−27 to 0.3n+15−27. Distributive property is used to expand 0.3(n+50) to 0.3n+15.
Simplify arithmetic operation: Step 2: Simplify 0.3n+15−27 to 0.3n−12. Simple arithmetic is used here, 15−27 equals −12.
Observe transformation: Step 3: Observe the transformation from 0.3n−12=0.1n−2 to 0.2n−12=−2. Subtraction property of equality is used to subtract 0.1n from both sides.
Solve linear equation: Step 4: Solve 0.2n−12=−2 to 0.2n=10. Addition property of equality is used to add 12 to both sides.
Final solution: Step 5: Solve 0.2n=10 to n=50. Division property of equality is used to divide both sides by 0.2.