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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)

1 answer

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

  1. Start by distributing the 3 in the term \(3(x + 5)\):

\[ 3(x + 5) = 3x + 15 \]

  1. Replace the right side of the equation:

\[ 4x = 3x + 15 - 15 \]

  1. Simplify the right side:

\[ 4x = 3x + 0 \]

This simplifies to:

\[ 4x = 3x \]

  1. Now, subtract \(3x\) from both sides:

\[ 4x - 3x = 0 \]

This gives:

\[ x = 0 \]

  1. Since we found a specific value for \(x\), the equation has one solution.

Thus, the solution is \(x = 0\) and the equation has one solution.