To solve the equation \(4(x - 4) = x - 13\) using inverse operations, follow these steps:
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Distribute the 4 on the left side: \[ 4 \cdot (x - 4) = 4x - 16 \] So, the equation becomes: \[ 4x - 16 = x - 13 \]
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Isolate the variable: To do this, we first want to get all the \(x\) terms on one side and the constant terms on the other side. We'll subtract \(x\) from both sides: \[ 4x - x - 16 = -13 \] This simplifies to: \[ 3x - 16 = -13 \]
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Add 16 to both sides to isolate the \(3x\): \[ 3x - 16 + 16 = -13 + 16 \] Simplifying this gives: \[ 3x = 3 \]
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Divide both sides by 3 to solve for \(x\): \[ x = \frac{3}{3} \] Therefore, we find: \[ x = 1 \]
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Check your solution by substituting \(x = 1\) back into the original equation: \[ 4(1 - 4) = 1 - 13 \] Simplifying both sides: \[ 4(-3) = -12 \quad \text{and} \quad -12 = -12 \] Since both sides are equal, our solution is verified.
So the final solution to the equation \(4(x - 4) = x - 13\) is: \[ \boxed{1} \]
If you have a sketch pad or graphing tool, you can represent each step visually, showing the distribution, moving terms from one side to the other, and isolating the variable.