Multiple choice

Solve the equation for r: 6|10r – 5| + 10 = 16

  1. { − 2 5 , 3 5 }

  2. { 2 5 , − 3 5 }

  3. { 2 5 , 3 4 }

  4. { 2 5 , 3 5 }

  5. { − 2 5 , − 3 5 }
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

6|10r - 5| + 10 = 16 implies 6|10r - 5| = 6, so |10r - 5| = 1. This gives two cases: 10r - 5 = 1 (10r = 6, r = 0.6 or 3/5) and 10r - 5 = -1 (10r = 4, r = 0.4 or 2/5).

AI explanation

First, subtract 10 from both sides of 6|10r - 5| + 10 = 16 to get 6|10r - 5| = 6, which simplifies to |10r - 5| = 1. This absolute value equation gives two possible cases: 10r - 5 = 1 or 10r - 5 = -1. For the first case, 10r = 6, so r = 3/5; for the second case, 10r = 4, so r = 2/5. The solution set is {2/5, 3/5}.

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