Question
Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15 (1 point)ResponsesThe equation has one solution: x=−10.The equation has one solution: x equals negative 10 .The equation has no solution.The equation has no solution.The equation has one solution: x=0.The equation has one solution: x equals 0 .The equation has infinite solutions.The equation has infinite solutions.
Answers
GPT-4o mini
Let's solve the equation \( 4x = 3(x + 5) - 15 \).
1. Distribute the \( 3 \) on the right side:
\[
4x = 3x + 15 - 15
\]
2. Simplify the right side:
\[
4x = 3x + 0
\]
\[
4x = 3x
\]
3. Subtract \( 3x \) from both sides:
\[
4x - 3x = 0
\]
\[
x = 0
\]
The equation has one solution: \( x = 0 \).
Therefore, the correct response is: **The equation has one solution: x equals 0.**
1. Distribute the \( 3 \) on the right side:
\[
4x = 3x + 15 - 15
\]
2. Simplify the right side:
\[
4x = 3x + 0
\]
\[
4x = 3x
\]
3. Subtract \( 3x \) from both sides:
\[
4x - 3x = 0
\]
\[
x = 0
\]
The equation has one solution: \( x = 0 \).
Therefore, the correct response is: **The equation has one solution: x equals 0.**