Algebra Examples

$\frac{2}{3} - \frac{7}{9} j + \frac{1}{3} j - \frac{1}{9} = 2 - j$

Step 1

Simplify $\frac{2}{3} - \frac{7}{9} j + \frac{1}{3} j - \frac{1}{9}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $j$ and $\frac{7}{9}$ .

$\frac{2}{3} - \frac{j \cdot 7}{9} + \frac{1}{3} j - \frac{1}{9} = 2 - j$

Step 1.1.2

Move $7$ to the left of $j$ .

$\frac{2}{3} - \frac{7 \cdot j}{9} + \frac{1}{3} j - \frac{1}{9} = 2 - j$

Step 1.1.3

Combine $\frac{1}{3}$ and $j$ .

$\frac{2}{3} - \frac{7 j}{9} + \frac{j}{3} - \frac{1}{9} = 2 - j$

Step 1.2

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

$- \frac{7 j}{9} + \frac{j}{3} + \frac{2}{3} \cdot \frac{3}{3} - \frac{1}{9} = 2 - j$

Step 1.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

$- \frac{7 j}{9} + \frac{j}{3} + \frac{2 \cdot 3}{3 \cdot 3} - \frac{1}{9} = 2 - j$

Step 1.3.2

Multiply $3$ by $3$ .

$- \frac{7 j}{9} + \frac{j}{3} + \frac{2 \cdot 3}{9} - \frac{1}{9} = 2 - j$

Step 1.4

Combine the numerators over the common denominator.

$- \frac{7 j}{9} + \frac{j}{3} + \frac{2 \cdot 3 - 1}{9} = 2 - j$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $3$ .

$- \frac{7 j}{9} + \frac{j}{3} + \frac{6 - 1}{9} = 2 - j$

Step 1.5.2

Subtract $1$ from $6$ .

$- \frac{7 j}{9} + \frac{j}{3} + \frac{5}{9} = 2 - j$

Step 1.6

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

$- \frac{7 j}{9} + \frac{j}{3} \cdot \frac{3}{3} + \frac{5}{9} = 2 - j$

Step 1.7

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.7.1

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

$- \frac{7 j}{9} + \frac{j \cdot 3}{3 \cdot 3} + \frac{5}{9} = 2 - j$

Step 1.7.2

Multiply $3$ by $3$ .

$- \frac{7 j}{9} + \frac{j \cdot 3}{9} + \frac{5}{9} = 2 - j$

Step 1.8

Simplify terms.

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Step 1.8.1

Combine the numerators over the common denominator.

$\frac{- 7 j + j \cdot 3}{9} + \frac{5}{9} = 2 - j$

Step 1.8.2

Combine the numerators over the common denominator.

$\frac{- 7 j + j \cdot 3 + 5}{9} = 2 - j$

Step 1.9

Move $3$ to the left of $j$ .

$\frac{- 7 j + 3 j + 5}{9} = 2 - j$

Step 1.10

Simplify terms.

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Step 1.10.1

Add $- 7 j$ and $3 j$ .

$\frac{- 4 j + 5}{9} = 2 - j$

Step 1.10.2

Factor $- 1$ out of $- 4 j$ .

$\frac{- (4 j) + 5}{9} = 2 - j$

Step 1.10.3

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{- (4 j) - 1 (- 5)}{9} = 2 - j$

Step 1.10.4

Factor $- 1$ out of $- (4 j) - 1 (- 5)$ .

$\frac{- (4 j - 5)}{9} = 2 - j$

Step 1.10.5

Simplify the expression.

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Step 1.10.5.1

Rewrite $- (4 j - 5)$ as $- 1 (4 j - 5)$ .

$\frac{- 1 (4 j - 5)}{9} = 2 - j$

Step 1.10.5.2

Move the negative in front of the fraction.

$- \frac{4 j - 5}{9} = 2 - j$

Step 2

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

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Step 2.1

Add $j$ to both sides of the equation.

$- \frac{4 j - 5}{9} + j = 2$

Step 2.2

To write $j$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{4 j - 5}{9} + j \cdot \frac{9}{9} = 2$

Step 2.3

Combine $j$ and $\frac{9}{9}$ .

$- \frac{4 j - 5}{9} + \frac{j \cdot 9}{9} = 2$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- (4 j - 5) + j \cdot 9}{9} = 2$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{- (4 j) - - 5 + j \cdot 9}{9} = 2$

Step 2.5.2

Multiply $4$ by $- 1$ .

$\frac{- 4 j - - 5 + j \cdot 9}{9} = 2$

Step 2.5.3

Multiply $- 1$ by $- 5$ .

$\frac{- 4 j + 5 + j \cdot 9}{9} = 2$

Step 2.5.4

Move $9$ to the left of $j$ .

$\frac{- 4 j + 5 + 9 \cdot j}{9} = 2$

Step 2.5.5

Add $- 4 j$ and $9 j$ .

$\frac{5 j + 5}{9} = 2$

Step 2.5.6

Factor $5$ out of $5 j + 5$ .

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Step 2.5.6.1

Factor $5$ out of $5 j$ .

$\frac{5 (j) + 5}{9} = 2$

Step 2.5.6.2

Factor $5$ out of $5$ .

$\frac{5 (j) + 5 (1)}{9} = 2$

Step 2.5.6.3

Factor $5$ out of $5 (j) + 5 (1)$ .

$\frac{5 (j + 1)}{9} = 2$

Step 3

Multiply both sides of the equation by $\frac{9}{5}$ .

$\frac{9}{5} \cdot \frac{5 (j + 1)}{9} = \frac{9}{5} \cdot 2$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{9}{5} \cdot \frac{5 (j + 1)}{9}$ .

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Step 4.1.1.1

Cancel the common factor of $9$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 (j + 1)}{9} = \frac{9}{5} \cdot 2$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 (j + 1)) = \frac{9}{5} \cdot 2$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{1}{5} (5 (j + 1)) = \frac{9}{5} \cdot 2$

Step 4.1.1.2.2

Rewrite the expression.

$j + 1 = \frac{9}{5} \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{9}{5} \cdot 2$ .

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Step 4.2.1.1

Combine $\frac{9}{5}$ and $2$ .

$j + 1 = \frac{9 \cdot 2}{5}$

Step 4.2.1.2

Multiply $9$ by $2$ .

$j + 1 = \frac{18}{5}$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the equation.

$j = \frac{18}{5} - 1$

Step 5.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$j = \frac{18}{5} - 1 \cdot \frac{5}{5}$

Step 5.3

Combine $- 1$ and $\frac{5}{5}$ .

$j = \frac{18}{5} + \frac{- 1 \cdot 5}{5}$

Step 5.4

Combine the numerators over the common denominator.

$j = \frac{18 - 1 \cdot 5}{5}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $- 1$ by $5$ .

$j = \frac{18 - 5}{5}$

Step 5.5.2

Subtract $5$ from $18$ .

$j = \frac{13}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$j = \frac{13}{5}$

Decimal Form:

$j = 2.6$

Mixed Number Form:

$j = 2 \frac{3}{5}$