Question
Complete the sentence based on the equation shown below.
h (-3x - 9) = -9 (x + 3)
This equation will have infinitely many solutions when h, = blank because you get infinitely many solutions when you have
number blank of x's on either side of the equation and blank
h (-3x - 9) = -9 (x + 3)
This equation will have infinitely many solutions when h, = blank because you get infinitely many solutions when you have
number blank of x's on either side of the equation and blank
Answers
Answer
Fill in the blank
Answered by
GPT-4o mini
This equation will have infinitely many solutions when \( h = -3 \) because you get infinitely many solutions when you have the same number of \( x \)'s on either side of the equation and the constants on both sides are equal as well.
To clarify:
1. If \( h = -3 \), then the left side becomes \( -3(-3x - 9) = 9x + 27 \).
2. The right side simplifies to \( -9(x + 3) = -9x - 27 \).
3. Setting these equal: \( 9x + 27 = -9x - 27 \).
4. Rearranging gives \( 18x + 54 = 0 \), leading to \( x = -3 \).
So, both sides lead to equivalent forms yielding solutions regardless of \( x \), hence infinitely many solutions.
To clarify:
1. If \( h = -3 \), then the left side becomes \( -3(-3x - 9) = 9x + 27 \).
2. The right side simplifies to \( -9(x + 3) = -9x - 27 \).
3. Setting these equal: \( 9x + 27 = -9x - 27 \).
4. Rearranging gives \( 18x + 54 = 0 \), leading to \( x = -3 \).
So, both sides lead to equivalent forms yielding solutions regardless of \( x \), hence infinitely many solutions.
Answered by
GPT-4o mini
This equation will have infinitely many solutions when \( h = -3 \) because you get infinitely many solutions when you have **the same number** of \( x \)'s on either side of the equation and **the same constants**.