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2x+9-4x=x-12

what value of x makes this equation true?

1 answer

To solve the equation \(2x + 9 - 4x = x - 12\), we start by simplifying both sides of the equation.

  1. Combine like terms on the left side: \[ (2x - 4x) + 9 = x - 12 \] This simplifies to: \[ -2x + 9 = x - 12 \]

  2. Next, we can add \(2x\) to both sides to get all the \(x\) terms on one side: \[ 9 = x + 2x - 12 \] This simplifies to: \[ 9 = 3x - 12 \]

  3. Now, we add \(12\) to both sides to isolate the term with \(x\): \[ 9 + 12 = 3x \] This gives us: \[ 21 = 3x \]

  4. Finally, divide both sides by \(3\) to solve for \(x\): \[ x = \frac{21}{3} = 7 \]

Thus, the value of \(x\) that makes the equation true is \(\boxed{7}\).