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When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step? Original Equation: -(1)/(4)x=1 First Step: x=-4 commutative property of addition associative property of multiplication multiplication property of equality distributive property of multiplication over addition

When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?\newlineOriginal Equation:\newline−14x=1 -\frac{1}{4} x=1 \newlineFirst Step:\newlinex=−4 x=-4 \newlinecommutative property of addition\newlineassociative property of multiplication\newlinemultiplication property of equality\newlinedistributive property of multiplication over addition

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Q. When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?\newlineOriginal Equation:\newline−14x=1 -\frac{1}{4} x=1 \newlineFirst Step:\newlinex=−4 x=-4 \newlinecommutative property of addition\newlineassociative property of multiplication\newlinemultiplication property of equality\newlinedistributive property of multiplication over addition
  1. Isolate variable x: Carmen's first step is to isolate the variable x on one side of the equation. To do this, she needs to get rid of the fraction −14-\frac{1}{4} that is multiplied by x. She does this by multiplying both sides of the equation by the reciprocal of −14-\frac{1}{4}, which is −4-4. This is shown in the first step:\newlineOriginal Equation: −14x=1-\frac{1}{4}x = 1\newlineFirst Step: x=−4x = -4\newlineThis step is justified by the multiplication property of equality, which states that if you multiply both sides of an equation by the same nonzero number, the two sides remain equal.\newlineCalculation: −14x⋅(−4)=1⋅(−4)-\frac{1}{4}x \cdot (-4) = 1 \cdot (-4)\newlinex = −4-4

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