Question
simplify "Both equations simplify to identities (statements that are always true)7x + 3 = 7x + 3: Subtracting 7x from both sides leaves 3 = 3, which is always true, regardless of x's value.3(4x + 8) = 4(3x + 6): Expanding both sides gives 12x + 24 = 12x + 24. Again, subtracting 12x from both sides leaves 24 = 24, a true statement for all x.Think of it like this: 3 = 3 is always true, no matter what number you substitute for x. These equations are just cleverly disguised versions of this simple truth"
Answers
GPT-4o mini
Both equations simplify to identities, meaning they are true for all values of \( x \).
1. **First equation:**
\( 7x + 3 = 7x + 3 \)
Subtracting \( 7x \) from both sides yields \( 3 = 3 \), which is always true.
2. **Second equation:**
\( 3(4x + 8) = 4(3x + 6) \)
Expanding both sides gives \( 12x + 24 = 12x + 24 \).
Subtracting \( 12x \) from both sides results in \( 24 = 24 \), also always true.
In essence, both equations ultimately reduce to the statement \( 3 = 3 \), which holds true for any value of \( x \).
1. **First equation:**
\( 7x + 3 = 7x + 3 \)
Subtracting \( 7x \) from both sides yields \( 3 = 3 \), which is always true.
2. **Second equation:**
\( 3(4x + 8) = 4(3x + 6) \)
Expanding both sides gives \( 12x + 24 = 12x + 24 \).
Subtracting \( 12x \) from both sides results in \( 24 = 24 \), also always true.
In essence, both equations ultimately reduce to the statement \( 3 = 3 \), which holds true for any value of \( x \).