Solve for n. {:[2-(1)/(2)n=3n+16],[n=◻]:}

Given system of equations: We are given a system of equations: 2 - (1/2)n = 3n + 16 n = ◻ Let's solve the first equation for n. First, we isolate the terms with n on one side of the equation.Solve for n: Subtract 2 from both sides of the equation to get: - (1/2)n = 3n + 14Subtract 2: Now, we need to get all the n terms on one side. We can do this by adding (1/2)n to both sides: 0 = 3n + (1/2)n + 14Combine like terms: Combine like terms on the right side of the equation: 0 = (3 + 1/2)n + 14 0 = (6/2 + 1/2)n + 14 0 = (7/2)n + 14Isolate the term: Now, subtract 14 from both sides to isolate the term with n: -14 = (7/2)nDivide by (7/2): To solve for n, divide both sides by (7/2): n = -14 / (7/2)Multiply by 2/7: Dividing by a fraction is the same as multiplying by its reciprocal. So, we multiply by 2/7: n = -14 * (2/7)Simplify the multiplication: Now, we simplify the multiplication: n = -28 / 7 n = -4

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Solve for
n.

{:[2-(1)/(2)n=3n+16],[n=◻]:}

Solve for $n$ . $\newline$ $\begin{array}{l} 2-\frac{1}{2} n=3 n+16 \\ n=\square \end{array}$

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Algebra 1

Solve linear equations with variables on both sides

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Q. Solve for

n

\newline

\begin{array}{l} 2-\frac{1}{2} n=3 n+16 \\ n=\square \end{array}

Given system of equations: We are given a system of equations: $\newline$ $2 - \frac{1}{2}n = 3n + 16$ $\newline$ $n = \square$ $\newline$ Let's solve the first equation for $n$ . $\newline$ First, we isolate the terms with $n$ on one side of the equation.
Solve for n: Subtract $2$ from both sides of the equation to get: $\newline$ $-\left(\frac{1}{2}\right)n = 3n + 14$
Subtract $2$ : Now, we need to get all the $n$ terms on one side. We can do this by adding $(1/2)n$ to both sides: $\newline$ $0 = 3n + (1/2)n + 14$
Combine like terms: Combine like terms on the right side of the equation: $\newline$ $0 = (3 + \frac{1}{2})n + 14$ $\newline$ $0 = (\frac{6}{2} + \frac{1}{2})n + 14$ $\newline$ $0 = (\frac{7}{2})n + 14$
Isolate the term: Now, subtract $14$ from both sides to isolate the term with $n$ : $-14 = \left(\frac{7}{2}\right)n$
Divide by $(7/2)$ : To solve for $n$ , divide both sides by $(7/2)$ : $n = -\frac{14}{(7/2)}$
Multiply by $2$ / $7$ : Dividing by a fraction is the same as multiplying by its reciprocal. So, we multiply by $2/7$ : $n = -14 \times \left(\frac{2}{7}\right)$
Simplify the multiplication: Now, we simplify the multiplication: $n = -\frac{28}{7}$ $n = -4$