Question
3(4x+8)=4(3x+6) how many solutions
Answers
GPT-4o mini
To solve the equation \( 3(4x + 8) = 4(3x + 6) \), we will first expand both sides:
1. Expand the left side:
\[
3(4x + 8) = 12x + 24
\]
2. Expand the right side:
\[
4(3x + 6) = 12x + 24
\]
Now we rewrite the equation:
\[
12x + 24 = 12x + 24
\]
Next, we subtract \( 12x \) from both sides:
\[
24 = 24
\]
This statement is always true. Since both sides of the equation are identical for any value of \( x \), it indicates that the equation is satisfied for all \( x \).
Therefore, the equation has **infinitely many solutions**.
1. Expand the left side:
\[
3(4x + 8) = 12x + 24
\]
2. Expand the right side:
\[
4(3x + 6) = 12x + 24
\]
Now we rewrite the equation:
\[
12x + 24 = 12x + 24
\]
Next, we subtract \( 12x \) from both sides:
\[
24 = 24
\]
This statement is always true. Since both sides of the equation are identical for any value of \( x \), it indicates that the equation is satisfied for all \( x \).
Therefore, the equation has **infinitely many solutions**.