Solve for x. 2(3-(2x+4))-5(x-7)=3x+1

Distribute 2 into parentheses: Distribute the 2 into the parentheses (3-(2x+4)). 2(3-(2x+4)) = 2*3 - 2*(2x+4) = 6 - 2*2x - 2*4 = 6 - 4x - 8Combine like terms: Combine like terms from the result of Step 1. 6 - 4x - 8 = -4x - 2Distribute -5 into parentheses: Distribute the -5 into the parentheses (x-7). -5(x-7) = -5*x + 5*7 = -5x + 35Combine results: Combine the results from Step 2 and Step 3. -4x - 2 - 5x + 35Combine like terms: Combine like terms from the result of Step 4. -4x - 5x = -9x -2 + 35 = 33 So, -4x - 2 - 5x + 35 = -9x + 33Write original equation: Write down the original equation with the simplified left side from Step 5. -9x + 33 = 3x + 1Move terms containing x: Move all terms containing x to one side of the equation. Add 9x to both sides. -9x + 33 + 9x = 3x + 1 + 9x 0 + 33 = 12x + 1Combine like terms: Combine like terms and isolate the variable x. 33 = 12x + 1 Subtract 1 from both sides. 33 - 1 = 12x + 1 - 1 32 = 12xDivide both sides: Divide both sides by 12 to solve for x. 32 / 12 = 12x / 12 x = 32 / 12 x = 8 / 3

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Solve for $x$ . $\newline$ $2(3-(2 x+4))-5(x-7)=3 x+1$

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Algebra 2

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2(3-(2 x+4))-5(x-7)=3 x+1

Distribute $2$ into parentheses: Distribute the $2$ into the parentheses $(3-(2x+4))$ . $2(3-(2x+4)) = 2\times3 - 2\times(2x+4)$ $= 6 - 2\times2x - 2\times4$ $= 6 - 4x - 8$
Combine like terms: Combine like terms from the result of Step $1$ . $\newline$ $6 - 4x - 8 = -4x - 2$
Distribute $-5$ into parentheses: Distribute the $-5$ into the parentheses $(x-7)$ . $\newline$ $-5(x-7) = -5\times x + 5\times 7$ $\newline$ $= -5x + 35$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $-4x - 2 - 5x + 35$
Combine like terms: Combine like terms from the result of Step $4$ . $\newline$ $-4x - 5x = -9x$ $\newline$ $-2 + 35 = 33$ $\newline$ So, $-4x - 2 - 5x + 35 = -9x + 33$
Write original equation: Write down the original equation with the simplified left side from Step $5$ . $\newline$ $-9x + 33 = 3x + 1$
Move terms containing $x$ : Move all terms containing $x$ to one side of the equation. $\newline$ Add $9x$ to both sides. $\newline$ $-9x + 33 + 9x = 3x + 1 + 9x$ $\newline$ $0 + 33 = 12x + 1$
Combine like terms: Combine like terms and isolate the variable $x$ . $\newline$ $33 = 12x + 1$ $\newline$ Subtract $1$ from both sides. $\newline$ $33 - 1 = 12x + 1 - 1$ $\newline$ $32 = 12x$
Divide both sides: Divide both sides by $12$ to solve for $x$ . $\newline$ $\frac{32}{12} = \frac{12x}{12}$ $\newline$ $x = \frac{32}{12}$ $\newline$ $x = \frac{8}{3}$