Algebra Examples

$5 j + \frac{2}{3} = - \frac{1}{6}$

Step 1

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

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Step 1.1

Subtract $\frac{2}{3}$ from both sides of the equation.

$5 j = - \frac{1}{6} - \frac{2}{3}$

Step 1.2

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 j = - \frac{1}{6} - \frac{2}{3} \cdot \frac{2}{2}$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$5 j = - \frac{1}{6} - \frac{2 \cdot 2}{3 \cdot 2}$

Step 1.3.2

Multiply $3$ by $2$ .

$5 j = - \frac{1}{6} - \frac{2 \cdot 2}{6}$

Step 1.4

Combine the numerators over the common denominator.

$5 j = \frac{- 1 - 2 \cdot 2}{6}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 2$ by $2$ .

$5 j = \frac{- 1 - 4}{6}$

Step 1.5.2

Subtract $4$ from $- 1$ .

$5 j = \frac{- 5}{6}$

Step 1.6

Move the negative in front of the fraction.

$5 j = - \frac{5}{6}$

Step 2

Divide each term in $5 j = - \frac{5}{6}$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 j = - \frac{5}{6}$ by $5$ .

$\frac{5 j}{5} = \frac{- \frac{5}{6}}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 j}{5} = \frac{- \frac{5}{6}}{5}$

Step 2.2.1.2

Divide $j$ by $1$ .

$j = \frac{- \frac{5}{6}}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$j = - \frac{5}{6} \cdot \frac{1}{5}$

Step 2.3.2

Cancel the common factor of $5$ .

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Step 2.3.2.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$j = \frac{- 5}{6} \cdot \frac{1}{5}$

Step 2.3.2.2

Factor $5$ out of $- 5$ .

$j = \frac{5 (- 1)}{6} \cdot \frac{1}{5}$

Step 2.3.2.3

Cancel the common factor.

$j = \frac{5 \cdot - 1}{6} \cdot \frac{1}{5}$

Step 2.3.2.4

Rewrite the expression.

$j = \frac{- 1}{6}$

Step 2.3.3

Move the negative in front of the fraction.

$j = - \frac{1}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$j = - \frac{1}{6}$

Decimal Form:

$j = - 0.1\overline{6}$