To solve the equation \( 2x - 5 = -10 + 3(4x + 5) \), we will follow these steps:
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Distribute on the right side: We need to distribute the \(3\) into the expression \(4x + 5\).
\[ 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \]
Now, we can rewrite the equation:
\[ 2x - 5 = -10 + 12x + 15 \]
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Combine like terms on the right side: \(-10 + 15\) simplifies to \(5\), so we have:
\[ 2x - 5 = 5 + 12x \]
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Isolate the variable \(x\): We want all the \(x\) terms on one side of the equation. We can subtract \(12x\) from both sides:
\[ 2x - 12x - 5 = 5 \]
This simplifies to:
\[ -10x - 5 = 5 \]
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Add \(5\) to both sides: To eliminate \(-5\) on the left side, we add \(5\) to both sides:
\[ -10x - 5 + 5 = 5 + 5 \]
This gives us:
\[ -10x = 10 \]
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Divide by \(-10\): To solve for \(x\), we divide both sides by \(-10\):
\[ x = \frac{10}{-10} = -1 \]
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Final answer: The solution to the equation is:
\[ \boxed{-1} \]
Explanation of Each Step:
- Step 1: Distributing \(3\) to \(4x + 5\) allows us to simplify the right-hand side of the equation.
- Step 2: Combining like terms helps to further simplify the equation into a more manageable form.
- Step 3-5: These steps involve rearranging the equation to isolate \(x\) through simple algebraic manipulations: moving terms from one side to the other and applying the properties of equality.
- Final answer: Providing the solution clearly as \(-1\).