Dylan solved this equation: x - x/5 = 6/5 5(x - x/5) = 5(6/5) 5x - x = 6 4x = 6 x = 3/2 Which property is not needed to justify any of the steps? Choices: (A)subtraction property of equality (B)multiplication property of equality (C)distributive property (D)division property of equality

Start with equation: Dylan starts with the equation x - x/5 = 6/5. Multiply to eliminate fraction: He multiplies every term by 5 to eliminate the fraction: 5(x - x/5) = 5(6/5). This uses the Multiplication Property of Equality. Simplify terms: Simplifying gives 5x - x = 6. This step involves simplifying each term, not applying a property of equality directly. Combine like terms: Combining like terms, 4x = 6. This step uses the Subtraction Property of Equality to combine x terms. Divide to solve for x: Finally, he divides both sides by 4 to solve for x: x = 3/2. This uses the Division Property of Equality.

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Dylan solved this equation: $\newline$ $x - \frac{x}{5} = \frac{6}{5}$ $\newline$ $5(x - \frac{x}{5}) = 5(\frac{6}{5})$ $\newline$ $5x - x = 6$ $\newline$ $4x = 6$ $\newline$ $x = \frac{3}{2}$ $\newline$ Which property is not needed to justify any of the steps? $\newline$ Choices: $\newline$ (A) subtraction property of equality $\newline$ (B) multiplication property of equality $\newline$ (C) distributive property $\newline$ (D) division property of equality

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Math Problems

Algebra 1

Properties of equality

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Q. Dylan solved this equation:

\newline

x - \frac{x}{5} = \frac{6}{5}

\newline

5(x - \frac{x}{5}) = 5(\frac{6}{5})

\newline

5x - x = 6

\newline

4x = 6

\newline

x = \frac{3}{2}

\newline

Which property is not needed to justify any of the steps?

\newline

Choices:

\newline

(A) subtraction property of equality

\newline

(B) multiplication property of equality

\newline

\newline

(D) division property of equality

Start with equation: Dylan starts with the equation $x - \frac{x}{5} = \frac{6}{5}$ .
Multiply to eliminate fraction: He multiplies every term by $5$ to eliminate the fraction: $5(x - \frac{x}{5}) = 5(\frac{6}{5})$ . This uses the Multiplication Property of Equality.
Simplify terms: Simplifying gives $5x - x = 6$ . This step involves simplifying each term, not applying a property of equality directly.
Combine like terms: Combining like terms, $4x = 6$ . This step uses the Subtraction Property of Equality to combine $x$ terms.
Divide to solve for $x$ : Finally, he divides both sides by $4$ to solve for $x$ : $x = \frac{3}{2}$ . This uses the Division Property of Equality.