Which expression is equivalent to 2(4x+7)-3(8x-4) ? (A) -16x+2 (B) -16x+26 (C) -20x+22 (D) 8x

Distribute 2 into terms: Distribute the 2 into the terms inside the first parentheses. 2(4x+7) becomes 2*4x + 2*7. Calculation: 2*4x = 8x and 2*7 = 14. So, 2(4x+7) = 8x + 14.Distribute -3 into terms: Distribute the -3 into the terms inside the second parentheses. -3(8x-4) becomes -3*8x + -3*(-4). Calculation: -3*8x = -24x and -3*(-4) = 12. So, -3(8x-4) = -24x + 12.Combine distributed results: Combine the results from Step 1 and Step 2. We have 8x + 14 from the first expression and -24x + 12 from the second expression. Combining them gives us (8x + 14) + (-24x + 12).Combine like terms: Combine like terms. 8x + (-24x) gives us -16x. 14 + 12 gives us 26. So, the combined expression is -16x + 26.

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Which expression is equivalent to 2(4x+7)-3(8x-4) ?
(A) -16x+2
(B) -16x+26
(C) -20x+22
(D) 8x

Which expression is equivalent to $2(4 x+7)-3(8 x-4)$ ? $\newline$ (A) $-16x+2$ $\newline$ (B) $-16x+26$ $\newline$ (C) $-20x+22$ $\newline$ (D) $8 x$

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Math Problems

Grade 7

Identify equivalent linear expressions I

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Q. Which expression is equivalent to

2(4 x+7)-3(8 x-4)

\newline

(A)

-16x+2

\newline

(B)

-16x+26

\newline

(C)

-20x+22

\newline

(D)

8 x

Distribute $2$ into terms: Distribute the $2$ into the terms inside the first parentheses. $2(4x+7)$ becomes $2\cdot4x + 2\cdot7$ . Calculation: $2\cdot4x = 8x$ and $2\cdot7 = 14$ . So, $2(4x+7) = 8x + 14$ .
Distribute $-3$ into terms: Distribute the $-3$ into the terms inside the second parentheses. $-3(8x-4)$ becomes $-3\times 8x + -3\times (-4)$ . Calculation: $-3\times 8x = -24x$ and $-3\times (-4) = 12$ . So, $-3(8x-4) = -24x + 12$ .
Combine distributed results: Combine the results from Step $1$ and Step $2$ . $\newline$ We have $8x + 14$ from the first expression and $-24x + 12$ from the second expression. $\newline$ Combining them gives us $(8x + 14) + (-24x + 12)$ .
Combine like terms: Combine like terms. $\newline$ $8x + (-24x)$ gives us $-16x$ . $\newline$ $14 + 12$ gives us $26$ . $\newline$ So, the combined expression is $-16x + 26$ .