(9)/(4)((10)/(3)x-4)-(1)/(4)(2x-8)

Distribute and Simplify: Simplify the first term (9/4)((10/3)x - 4). We need to distribute (9/4) across the terms inside the parentheses. (9/4)((10/3)x - 4) = (9/4)*(10/3)x - (9/4)*4Simplify Coefficients for x: Simplify the multiplication of the coefficients for the x term. (9/4)*(10/3)x = (9*10)/(4*3)x = 90/12x = 7.5xSimplify Constant Term: Simplify the constant term in the first expression. (9/4)*4 = 9Combine Results: Combine the results from Step 2 and Step 3. (9/4)((10/3)x - 4) = 7.5x - 9Distribute and Simplify: Simplify the second term (1/4)(2x - 8). We need to distribute (1/4) across the terms inside the parentheses. (1/4)(2x - 8) = (1/4)*2x - (1/4)*8Simplify Coefficients for x: Simplify the multiplication of the coefficients for the x term. (1/4)*2x = (1*2)/(4*1)x = 2/4x = 0.5xSimplify Constant Term: Simplify the constant term in the second expression. (1/4)*8 = 2Combine Results: Combine the results from Step 6 and Step 7. (1/4)(2x - 8) = 0.5x - 2Subtract Expressions: Subtract the second expression from the first. (7.5x - 9) - (0.5x - 2) = 7.5x - 0.5x - 9 + 2Combine Like Terms: Combine like terms. 7.5x - 0.5x = 7x -9 + 2 = -7Write Final Expression: Write the final simplified expression. 7x - 7

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$\frac{9}{4}\left(\frac{10}{3} x-4\right)-\frac{1}{4}(2 x-8)$

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\frac{9}{4}\left(\frac{10}{3} x-4\right)-\frac{1}{4}(2 x-8)

Distribute and Simplify: Simplify the first term $(\frac{9}{4})((\frac{10}{3})x - 4)$ . We need to distribute $(\frac{9}{4})$ across the terms inside the parentheses. (\frac{$9$}{$4$})((\frac{$10$}{$3$})x - \(4) = (\frac{ $9$ }{ $4$ })\cdot(\frac{ $10$ }{ $3$ })x - (\frac{ $9$ }{ $4$ })\cdot $4$
Simplify Coefficients for $x$ : Simplify the multiplication of the coefficients for the $x$ term. $\left(\frac{9}{4}\right)\cdot\left(\frac{10}{3}\right)x = \frac{9\cdot10}{4\cdot3}x = \frac{90}{12}x = 7.5x$
Simplify Constant Term: Simplify the constant term in the first expression. $\newline$ $(\frac{9}{4})\cdot 4 = 9$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(\frac{9}{4})((\frac{10}{3})x - 4) = 7.5x - 9$
Distribute and Simplify: Simplify the second term $(\frac{1}{4})(2x - 8)$ . We need to distribute $(\frac{1}{4})$ across the terms inside the parentheses. (\frac{$1$}{$4$})(\(2x - $8$ ) = (\frac{ $1$ }{ $4$ })\cdot $2$ x - (\frac{ $1$ }{ $4$ })\cdot $8$
Simplify Coefficients for $x$ : Simplify the multiplication of the coefficients for the $x$ term. $\newline$ (\frac{$1$}{$4$})\cdot \(2x = (\frac{ $1$ \cdot $2$ }{ $4$ \cdot $1$ })x = \frac{ $2$ }{ $4$ }x = $0$ . $5$ x
Simplify Constant Term: Simplify the constant term in the second expression. $\newline$ $(\frac{1}{4})\times 8 = 2$
Combine Results: Combine the results from Step $6$ and Step $7$ . $\newline$ $(\frac{1}{4})(2x - 8) = 0.5x - 2$
Subtract Expressions: Subtract the second expression from the first. $\newline$ $(7.5x - 9) - (0.5x - 2) = 7.5x - 0.5x - 9 + 2$
Combine Like Terms: Combine like terms. $\newline$ $7.5x - 0.5x = 7x$ $\newline$ $-9 + 2 = -7$
Write Final Expression: Write the final simplified expression. $7x - 7$