Algebra Examples

$\frac{5}{6} (12 n - 18) = 17 + 10 n$

Step 1

Simplify $\frac{5}{6} \cdot (12 n - 18)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{5}{6} \cdot (12 n - 18) = 17 + 10 n$

Step 1.2

Simplify by adding zeros.

$\frac{5}{6} \cdot (12 n - 18) = 17 + 10 n$

Step 1.3

Apply the distributive property.

$\frac{5}{6} (12 n) + \frac{5}{6} \cdot - 18 = 17 + 10 n$

Step 1.4

Cancel the common factor of $6$ .

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Step 1.4.1

Factor $6$ out of $12 n$ .

$\frac{5}{6} (6 (2 n)) + \frac{5}{6} \cdot - 18 = 17 + 10 n$

Step 1.4.2

Cancel the common factor.

$\frac{5}{6} (6 (2 n)) + \frac{5}{6} \cdot - 18 = 17 + 10 n$

Step 1.4.3

Rewrite the expression.

$5 (2 n) + \frac{5}{6} \cdot - 18 = 17 + 10 n$

Step 1.5

Multiply $2$ by $5$ .

$10 n + \frac{5}{6} \cdot - 18 = 17 + 10 n$

Step 1.6

Cancel the common factor of $6$ .

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Step 1.6.1

Factor $6$ out of $- 18$ .

$10 n + \frac{5}{6} \cdot (6 (- 3)) = 17 + 10 n$

Step 1.6.2

Cancel the common factor.

$10 n + \frac{5}{6} \cdot (6 \cdot - 3) = 17 + 10 n$

Step 1.6.3

Rewrite the expression.

$10 n + 5 \cdot - 3 = 17 + 10 n$

Step 1.7

Multiply $5$ by $- 3$ .

$10 n - 15 = 17 + 10 n$

Step 2

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

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Step 2.1

Subtract $10 n$ from both sides of the equation.

$10 n - 15 - 10 n = 17$

Step 2.2

Combine the opposite terms in $10 n - 15 - 10 n$ .

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Step 2.2.1

Subtract $10 n$ from $10 n$ .

$0 - 15 = 17$

Step 2.2.2

Subtract $15$ from $0$ .

$- 15 = 17$

Step 3

Since $- 15 \neq 17$ , there are no solutions.

No solution