To solve the equation \( 2x - 5 = 3(4x + 5) \) step by step, follow these steps:
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Distribute on the right side: Start by distributing the \( 3 \) to both terms inside the parentheses on the right side of the equation. \[ 2x - 5 = 3 \cdot 4x + 3 \cdot 5 \] This simplifies to: \[ 2x - 5 = 12x + 15 \]
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Combine like terms: Next, we want to isolate \( x \). Start by moving all terms involving \( x \) to one side and the constant terms to the other side. To do this, subtract \( 12x \) from both sides: \[ 2x - 12x - 5 = 15 \] This simplifies to: \[ -10x - 5 = 15 \]
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Add constant terms: Now, add \( 5 \) to both sides to move the constant term: \[ -10x - 5 + 5 = 15 + 5 \] This simplifies to: \[ -10x = 20 \]
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Solve for \( x \): Finally, divide both sides by \( -10 \) to isolate \( x \): \[ x = \frac{20}{-10} \] This simplifies to: \[ x = -2 \]
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Check the solution (optional but recommended): Substitute \( x = -2 \) back into the original equation to verify: \[ 2(-2) - 5 = 3(4(-2) + 5) \] This simplifies to: \[ -4 - 5 = 3(-8 + 5) \] Which further simplifies to: \[ -9 = 3(-3) \] Thus: \[ -9 = -9 \quad \text{(True)} \]
So the solution is \( x = -2 \).
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