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Solve for x

to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15
(1 point)
Responses

The equation has no solution.
The equation has no solution.

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .

The equation has one solution: x=−10
.

1 answer

To solve the equation \( 4x = 3(x+5) - 15 \), we can follow these steps:

  1. Distribute the \(3\) on the right side: \[ 3(x + 5) = 3x + 15 \] So, the equation becomes: \[ 4x = 3x + 15 - 15 \] Simplifying the right side gives: \[ 4x = 3x \]

  2. Now, we isolate \(x\) by subtracting \(3x\) from both sides: \[ 4x - 3x = 0 \] This simplifies to: \[ x = 0 \]

Since we have found a unique solution (one solution), the answer is:

The equation has one solution: \( x = 0 \).