Which of the following expressions is equivalent to (-5k-10)/(40 k+45) ? Choose 1 answer: (A) (k+2)/(8k+9) (B) (-k-2)/(8k-9) (C) (-k-2)/(8k+9) (D) (-k+2)/(8k+9)

Factor out common factors: Factor out the greatest common factor in the numerator and the denominator. The greatest common factor in the numerator is 5, and in the denominator, it is 5 as well. Let's factor them out. (-5k - 10) can be factored as -5(k + 2). (40k + 45) can be factored as 5(8k + 9). So, the expression becomes: (-5(k + 2))/(5(8k + 9))Simplify expression: Simplify the expression by canceling out the common factors. The -5 in the numerator and the 5 in the denominator can be canceled out because they are common factors. This simplification gives us: -(k + 2)/(8k + 9)Check answer choices: Check the answer choices to see which one matches our simplified expression. The expression we have is -(k + 2)/(8k + 9), which matches choice (C).

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Which of the following expressions is equivalent to
(-5k-10)/(40 k+45) ?
Choose 1 answer:
(A)
(k+2)/(8k+9)
(B)
(-k-2)/(8k-9)
(C)
(-k-2)/(8k+9)
(D)
(-k+2)/(8k+9)

Which of the following expressions is equivalent to $\frac{-5 k-10}{40 k+45}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{k+2}{8 k+9}$ $\newline$ (B) $\frac{-k-2}{8 k-9}$ $\newline$ (C) $\frac{-k-2}{8 k+9}$ $\newline$ (D) $\frac{-k+2}{8 k+9}$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following expressions is equivalent to

\frac{-5 k-10}{40 k+45}

\newline

Choose

1

answer:

\newline

(A)

\frac{k+2}{8 k+9}

\newline

(B)

\frac{-k-2}{8 k-9}

\newline

(C)

\frac{-k-2}{8 k+9}

\newline

(D)

\frac{-k+2}{8 k+9}

Factor out common factors: Factor out the greatest common factor in the numerator and the denominator. $\newline$ The greatest common factor in the numerator is $5$ , and in the denominator, it is $5$ as well. Let's factor them out. $\newline$ $(-5k - 10)$ can be factored as $-5(k + 2)$ . $\newline$ $(40k + 45)$ can be factored as $5(8k + 9)$ . $\newline$ So, the expression becomes: $\newline$ $\frac{-5(k + 2)}{5(8k + 9)}$
Simplify expression: Simplify the expression by canceling out the common factors. $\newline$ The $-5$ in the numerator and the $5$ in the denominator can be canceled out because they are common factors. $\newline$ This simplification gives us: $\newline$ $-\frac{(k + 2)}{(8k + 9)}$
Check answer choices: Check the answer choices to see which one matches our simplified expression. $\newline$ The expression we have is $-\frac{{k + 2}}{{8k + 9}}$ , which matches choice (C).