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SAT Math Question of the Day

SAT Math Question of the Day

Answer today's SAT Math question, reveal the full explanation, then keep the streak going with a new question every day.

If 4(3x−2)+k=12x+54(3x-2)+k = 12x+54(3x−2)+k=12x+5, what is the value of kkk? Distribute first, then compare constants on both sides.

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Question of the Day

If 4(3x−2)+k=12x+54(3x-2)+k = 12x+54(3x−2)+k=12x+5, what is the value of kkk? Distribute first, then compare constants on both sides.

  1. 333
  2. −3-3−3
  3. −13-13−13
  4. 131313 (correct answer)

Explanation: We need to find kkk in the equation 4(3x−2)+k=12x+54(3x-2)+k = 12x+54(3x−2)+k=12x+5. First, distribute on the left side: 4(3x−2)=12x−84(3x-2) = 12x - 84(3x−2)=12x−8. So the equation becomes 12x−8+k=12x+512x - 8 + k = 12x + 512x−8+k=12x+5. Since the xxx terms are equal on both sides, we can compare constants: −8+k=5-8 + k = 5−8+k=5, which gives us k=13k = 13k=13. The key insight is that once we have the same coefficient for xxx on both sides, we only need to match the constant terms. This type of problem tests your ability to recognize when expressions are equivalent.