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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)

The equation has one solution: x=−10.

The equation has no solution.

The equation has infinite solutions.

The equation has one solution: x=0.

1 answer

To solve the equation \( 4x = 3(x + 5) - 15 \), we first simplify the right side.

  1. Expand the right side: \[ 3(x + 5) = 3x + 15 \] Therefore, \[ 3(x + 5) - 15 = 3x + 15 - 15 = 3x \]

  2. Now the equation becomes: \[ 4x = 3x \]

  3. To isolate \( x \), subtract \( 3x \) from both sides: \[ 4x - 3x = 0 \implies x = 0 \]

Now, let's determine the types of solutions. Since we found a specific value for \( x \) (which is 0), the equation has one solution.

So the answer is: The equation has one solution: \( x = 0 \).