Pregunta
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Which of the following equations have no solutions? Choose all answers that apply: A \( 33 x+25=33 x+25 \) B \( 33 x+33=33 x+25 \) C \( 33 x-25=33 x+25 \) (D) \( 33 x-33=33 x+25 \)

Ask by Carlson Ayala. in the United States
Feb 27,2025

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The equations with no solutions are B, C, and D.

Solución

Let's examine each equation by simplifying them. A) 33x + 25 = 33x + 25 Subtract 33x from both sides: 25 = 25, which is always true. This equation has infinitely many solutions. B) 33x + 33 = 33x + 25 Subtract 33x from both sides: 33 = 25, which is false. Therefore, this equation has no solutions. C) 33x - 25 = 33x + 25 Subtract 33x from both sides: -25 = 25, which is false. Therefore, this equation has no solutions. D) 33x - 33 = 33x + 25 Subtract 33x from both sides: -33 = 25, which is false. Therefore, this equation has no solutions. Thus, the equations that have no solutions are: B, C, and D.

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The Deep Dive

Let's break it down! For option A, \( 33 x + 25 = 33 x + 25 \), this is always true for any value of \( x \) because it's identical on both sides. It's like saying "apples are apples," so it has infinite solutions. For option B, \( 33 x + 33 = 33 x + 25 \), simplifying gives us \( 33 = 25 \), which is obviously false. Hence, this equation has no solutions. Option C, \( 33 x - 25 = 33 x + 25 \), simplifies to \( -25 = 25 \), which, again, is false. Thus, this one also has no solutions. Finally, option D, \( 33 x - 33 = 33 x + 25 \), simplifies to \( -33 = 25 \), which is also not correct. Hence, this too has no solutions. So, the equations with no solutions are B, C, and D! How’s that for some equation sleuthing?

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