Solve 2x + \{4 + 1(x - 4) + 1\} = 1/3 * \{5(2x + 3) + 2\} - 8

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Question

$$2x+\{4+1(x-4)+1\}=\frac{1}{3}\{5(2x+3)+2\}-8$$

Solve for x

$x=10$

Steps for Solving Linear Equation

Use the distributive property to multiply $1$ by $x-4$.

$$2x+4+x-4+1=\frac{1}{3}\left(5\left(2x+3\right)+2\right)-8$$

Combine $2x$ and $x$ to get $3x$.

$$3x+4-4+1=\frac{1}{3}\left(5\left(2x+3\right)+2\right)-8$$

Subtract $4$ from $4$ to get $0$.

$$3x+1=\frac{1}{3}\left(5\left(2x+3\right)+2\right)-8$$

Use the distributive property to multiply $5$ by $2x+3$.

$$3x+1=\frac{1}{3}\left(10x+15+2\right)-8$$

Add $15$ and $2$ to get $17$.

$$3x+1=\frac{1}{3}\left(10x+17\right)-8$$

Use the distributive property to multiply $\frac{1}{3}$ by $10x+17$.

$$3x+1=\frac{1}{3}\times 10x+\frac{1}{3}\times 17-8$$

Multiply $\frac{1}{3}$ and $10$ to get $\frac{10}{3}$.

$$3x+1=\frac{10}{3}x+\frac{1}{3}\times 17-8$$

Multiply $\frac{1}{3}$ and $17$ to get $\frac{17}{3}$.

$$3x+1=\frac{10}{3}x+\frac{17}{3}-8$$

Convert $8$ to fraction $\frac{24}{3}$.

$$3x+1=\frac{10}{3}x+\frac{17}{3}-\frac{24}{3}$$

Since $\frac{17}{3}$ and $\frac{24}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$3x+1=\frac{10}{3}x+\frac{17-24}{3}$$

Subtract $24$ from $17$ to get $-7$.

$$3x+1=\frac{10}{3}x-\frac{7}{3}$$

Subtract $\frac{10}{3}x$ from both sides.

$$3x+1-\frac{10}{3}x=-\frac{7}{3}$$

Combine $3x$ and $-\frac{10}{3}x$ to get $-\frac{1}{3}x$.

$$-\frac{1}{3}x+1=-\frac{7}{3}$$

Subtract $1$ from both sides.

$$-\frac{1}{3}x=-\frac{7}{3}-1$$

Convert $1$ to fraction $\frac{3}{3}$.

$$-\frac{1}{3}x=-\frac{7}{3}-\frac{3}{3}$$

Since $-\frac{7}{3}$ and $\frac{3}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}x=\frac{-7-3}{3}$$

Subtract $3$ from $-7$ to get $-10$.

$$-\frac{1}{3}x=-\frac{10}{3}$$

Multiply both sides by $-3$, the reciprocal of $-\frac{1}{3}$.

$$x=-\frac{10}{3}\left(-3\right)$$

Express $-\frac{10}{3}\left(-3\right)$ as a single fraction.

$$x=\frac{-10\left(-3\right)}{3}$$

Multiply $-10$ and $-3$ to get $30$.

$$x=\frac{30}{3}$$

Divide $30$ by $3$ to get $10$.

$$x=10$$

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