Question
Which of the statements is true for the two equations below?
Equation A: 3(2x-5)=6x-15
Equation B: 2+3x=3x-4
Equation A: 3(2x-5)=6x-15
Equation B: 2+3x=3x-4
Answers
Answered by
GPT-4o mini
Let's analyze both equations one by one to determine their validity.
**Equation A:**
\[ 3(2x - 5) = 6x - 15 \]
First, simplify the left side:
\[ 3(2x) - 3(5) = 6x - 15 \]
\[ 6x - 15 = 6x - 15 \]
This simplifies to:
\[ 6x - 15 = 6x - 15 \]
This is a true statement for all values of \( x \). Therefore, Equation A is an identity (true for all \( x \)).
**Equation B:**
\[ 2 + 3x = 3x - 4 \]
Now, let's simplify this equation by trying to isolate \( x \):
Subtract \( 3x \) from both sides:
\[ 2 = -4 \]
This is a contradiction since \( 2 \) does not equal \( -4 \). Therefore, Equation B has no solutions.
**Conclusion:**
Equation A is true for all values of \( x \) (it is an identity), while Equation B has no solutions. Thus, the true statement regarding the two equations is that Equation A holds true for all \( x \), and Equation B does not hold for any \( x \).
**Equation A:**
\[ 3(2x - 5) = 6x - 15 \]
First, simplify the left side:
\[ 3(2x) - 3(5) = 6x - 15 \]
\[ 6x - 15 = 6x - 15 \]
This simplifies to:
\[ 6x - 15 = 6x - 15 \]
This is a true statement for all values of \( x \). Therefore, Equation A is an identity (true for all \( x \)).
**Equation B:**
\[ 2 + 3x = 3x - 4 \]
Now, let's simplify this equation by trying to isolate \( x \):
Subtract \( 3x \) from both sides:
\[ 2 = -4 \]
This is a contradiction since \( 2 \) does not equal \( -4 \). Therefore, Equation B has no solutions.
**Conclusion:**
Equation A is true for all values of \( x \) (it is an identity), while Equation B has no solutions. Thus, the true statement regarding the two equations is that Equation A holds true for all \( x \), and Equation B does not hold for any \( x \).