Solve for n 4(8n+3)-5=2(6n+8)+1

$4 (8 n + 3) - 5 = 2 (6 n + 8) + 1$

Step 1

Simplify $4 (8 n + 3) - 5$ .

Simplify each term.

Apply the distributive property.

$4 (8 n) + 4 \cdot 3 - 5 = 2 (6 n + 8) + 1$

Multiply $8$ by $4$ .

$32 n + 4 \cdot 3 - 5 = 2 (6 n + 8) + 1$

Multiply $4$ by $3$ .

$32 n + 12 - 5 = 2 (6 n + 8) + 1$

Subtract $5$ from $12$ .

$32 n + 7 = 2 (6 n + 8) + 1$

Step 2

Simplify $2 (6 n + 8) + 1$ .

Simplify each term.

Apply the distributive property.

$32 n + 7 = 2 (6 n) + 2 \cdot 8 + 1$

Multiply $6$ by $2$ .

$32 n + 7 = 12 n + 2 \cdot 8 + 1$

Multiply $2$ by $8$ .

$32 n + 7 = 12 n + 16 + 1$

Add $16$ and $1$ .

$32 n + 7 = 12 n + 17$

Step 3

Move all terms containing $n$ to the left side of the equation.

Subtract $12 n$ from both sides of the equation.

$32 n + 7 - 12 n = 17$

Subtract $12 n$ from $32 n$ .

$20 n + 7 = 17$

Step 4

Move all terms not containing $n$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$20 n = 17 - 7$

Subtract $7$ from $17$ .

$20 n = 10$

Step 5

Divide each term in $20 n = 10$ by $20$ and simplify.

Divide each term in $20 n = 10$ by $20$ .

$\frac{20 n}{20} = \frac{10}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 n}{20} = \frac{10}{20}$

Divide $n$ by $1$ .

$n = \frac{10}{20}$

Simplify the right side.

Cancel the common factor of $10$ and $20$ .

Factor $10$ out of $10$ .

$n = \frac{10 (1)}{20}$

Cancel the common factors.

Factor $10$ out of $20$ .

$n = \frac{10 \cdot 1}{10 \cdot 2}$

Cancel the common factor.

$n = \frac{10 \cdot 1}{10 \cdot 2}$

Rewrite the expression.

$n = \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$n = \frac{1}{2}$

Decimal Form:

$n = 0.5$

Solve for n 4(8n+3)-5=2(6n+8)+1

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