Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Naomi solved this equation:\newline0.3(n+50)27=0.1(n20)0.3(n + 50) - 27 = 0.1(n - 20)\newline0.3n+1527=0.1n20.3n + 15 - 27 = 0.1n - 2\newline0.3n12=0.1n20.3n - 12 = 0.1n - 2\newline0.2n12=20.2n - 12 = -2\newline0.2n=100.2n = 10\newlinen=50n = 50\newlineWhich property is not needed to justify any of the steps?\newlineChoices:\newline(A) division property of equality\newline(B) commutative property of multiplication\newline(C) addition property of equality\newline(D) distributive property

Full solution

Q. Naomi solved this equation:\newline0.3(n+50)27=0.1(n20)0.3(n + 50) - 27 = 0.1(n - 20)\newline0.3n+1527=0.1n20.3n + 15 - 27 = 0.1n - 2\newline0.3n12=0.1n20.3n - 12 = 0.1n - 2\newline0.2n12=20.2n - 12 = -2\newline0.2n=100.2n = 10\newlinen=50n = 50\newlineWhich property is not needed to justify any of the steps?\newlineChoices:\newline(A) division property of equality\newline(B) commutative property of multiplication\newline(C) addition property of equality\newline(D) distributive property
  1. Analyze equation transformation: Step 11: Analyze the equation transformation from 0.3(n+50)270.3(n + 50) - 27 to 0.3n+15270.3n + 15 - 27. Distributive property is used to expand 0.3(n+50)0.3(n + 50) to 0.3n+150.3n + 15.
  2. Simplify arithmetic operation: Step 22: Simplify 0.3n+15270.3n + 15 - 27 to 0.3n120.3n - 12. Simple arithmetic is used here, 152715 - 27 equals 12-12.
  3. Observe transformation: Step 33: Observe the transformation from 0.3n12=0.1n20.3n - 12 = 0.1n - 2 to 0.2n12=20.2n - 12 = -2. Subtraction property of equality is used to subtract 0.1n0.1n from both sides.
  4. Solve linear equation: Step 44: Solve 0.2n12=20.2n - 12 = -2 to 0.2n=100.2n = 10. Addition property of equality is used to add 1212 to both sides.
  5. Final solution: Step 55: Solve 0.2n=100.2n = 10 to n=50n = 50. Division property of equality is used to divide both sides by 0.20.2.

More problems from Properties of equality