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When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step? Original Equation: (1)/(3)x=3 First Step: x=9 addition property of equality multiplication property of equality commutative property of multiplication subtraction property of equality

When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?\newlineOriginal Equation:\newline13x=3 \frac{1}{3} x=3 \newlineFirst Step:\newlinex=9 x=9 \newlineaddition property of equality\newlinemultiplication property of equality\newlinecommutative property of multiplication\newlinesubtraction property of equality

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Q. When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?\newlineOriginal Equation:\newline13x=3 \frac{1}{3} x=3 \newlineFirst Step:\newlinex=9 x=9 \newlineaddition property of equality\newlinemultiplication property of equality\newlinecommutative property of multiplication\newlinesubtraction property of equality
  1. Initial Equation: Gabrielle's first step in solving the equation is to go from (13)x=3(\frac{1}{3})x = 3 to x=9x = 9. To justify this step, we need to determine which property allows us to go from the original equation to the first step. Let's analyze the step:\newlineOriginal Equation: (13)x=3(\frac{1}{3})x = 3\newlineFirst Step: x=9x = 9\newlineTo isolate xx, we need to eliminate the fraction (13)(\frac{1}{3}) that is being multiplied by xx. To do this, we can multiply both sides of the equation by the reciprocal of (13)(\frac{1}{3}), which is 33. This is because multiplying by the reciprocal will cancel out the (13)(\frac{1}{3}) on the left side, leaving us with just xx.\newlineCalculation:\newlinex=9x = 911\newlinex=9x = 9\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.

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