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Question Solve the following equation for \( x \). \[ -12+7 x-5 x=4-3 x+2 \] Give your answer as an improper fraction, if necessary.

Ask by Kirk Montgomery. in the United States
Feb 12,2025

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\( x = \frac{18}{5} \)

Solución

Solve the equation \( -12+7x-5x=4-3x+2 \). Solve the equation by following steps: - step0: Solve for \(x\): \(-12+7x-5x=4-3x+2\) - step1: Subtract the terms: \(-12+2x=6-3x\) - step2: Move the expression to the left side: \(2x+3x=6+12\) - step3: Add and subtract: \(5x=6+12\) - step4: Add and subtract: \(5x=18\) - step5: Divide both sides: \(\frac{5x}{5}=\frac{18}{5}\) - step6: Divide the numbers: \(x=\frac{18}{5}\) The solution to the equation \( -12+7x-5x=4-3x+2 \) is \( x = \frac{18}{5} \) or \( x = 3.6 \).

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Bonus Knowledge

To solve the equation \(-12 + 7x - 5x = 4 - 3x + 2\), we first simplify both sides of the equation: Combine like terms on the left: \[ -12 + (7x - 5x) = -12 + 2x \] Combine like terms on the right: \[ 4 + 2 = 6 - 3x \] Now the equation is: \[ -12 + 2x = 6 - 3x \] Next, let's move all \(x\) terms to one side and constant terms to the other side. We'll add \(3x\) and \(12\) to both sides: \[ 2x + 3x = 6 + 12 \] \[ 5x = 18 \] Now, divide by \(5\): \[ x = \frac{18}{5} \] Thus, the solution for \(x\) is \(\frac{18}{5}\).

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