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When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step? Original Equation: 2(x+1)=4 First Step: 2x+2=4 addition property of equality associative property of multiplication distributive property of multiplication over addition commutative property of addition

When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?\newlineOriginal Equation:\newline2(x+1)=4 2(x+1)=4 \newlineFirst Step:\newline2x+2=4 2 x+2=4 \newlineaddition property of equality\newlineassociative property of multiplication\newlinedistributive property of multiplication over addition\newlinecommutative property of addition

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Full solution

Q. When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?\newlineOriginal Equation:\newline2(x+1)=4 2(x+1)=4 \newlineFirst Step:\newline2x+2=4 2 x+2=4 \newlineaddition property of equality\newlineassociative property of multiplication\newlinedistributive property of multiplication over addition\newlinecommutative property of addition
  1. Transform Original Equation: Gabrielle's first step is to go from the original equation 2(x+1)=42(x+1)=4 to the equation 2x+2=42x+2=4. To determine which property justifies this step, we need to look at the transformation that has been applied to the original equation. Gabrielle has taken the term 2(x+1)2(x+1) and turned it into 2x+22x+2. This is done by applying a property of operations to the terms inside the parentheses.
  2. Apply Distributive Property: The distributive property of multiplication over addition states that a(b+c)=ab+aca(b+c) = ab + ac. In the context of the equation, 2(x+1)2(x+1) can be distributed to become 2×x+2×12\times x + 2\times 1, which simplifies to 2x+22x + 2. This is exactly what Gabrielle did in her first step.
  3. Verify Math Accuracy: To check for any math errors, we can apply the distributive property ourselves to the original equation: 2(x+1)=2×x+2×1=2x+22(x+1) = 2\times x + 2\times 1 = 2x + 2. This matches Gabrielle's first step, confirming that there are no math errors in this step.

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