Algebra Examples

$\frac{2}{5} (10 j - 25 + 15 j) - \frac{3}{2} (6 j - 4) = - 2 j$

Step 1

Simplify $\frac{2}{5} \cdot (10 j - 25 + 15 j) - \frac{3}{2} \cdot (6 j - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Add $10 j$ and $15 j$ .

$\frac{2}{5} \cdot (25 j - 25) - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.2

Apply the distributive property.

$\frac{2}{5} (25 j) + \frac{2}{5} \cdot - 25 - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.3

Cancel the common factor of $5$ .

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Step 1.1.3.1

Factor $5$ out of $25 j$ .

$\frac{2}{5} (5 (5 j)) + \frac{2}{5} \cdot - 25 - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.3.2

Cancel the common factor.

$\frac{2}{5} (5 (5 j)) + \frac{2}{5} \cdot - 25 - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.3.3

Rewrite the expression.

$2 (5 j) + \frac{2}{5} \cdot - 25 - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.4

Multiply $5$ by $2$ .

$10 j + \frac{2}{5} \cdot - 25 - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.5

Cancel the common factor of $5$ .

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Step 1.1.5.1

Factor $5$ out of $- 25$ .

$10 j + \frac{2}{5} \cdot (5 (- 5)) - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.5.2

Cancel the common factor.

$10 j + \frac{2}{5} \cdot (5 \cdot - 5) - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.5.3

Rewrite the expression.

$10 j + 2 \cdot - 5 - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.6

Multiply $2$ by $- 5$ .

$10 j - 10 - \frac{3}{2} \cdot (6 j - 4) = - 2 j$

Step 1.1.7

Apply the distributive property.

$10 j - 10 - \frac{3}{2} (6 j) - \frac{3}{2} \cdot - 4 = - 2 j$

Step 1.1.8

Cancel the common factor of $2$ .

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Step 1.1.8.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$10 j - 10 + \frac{- 3}{2} (6 j) - \frac{3}{2} \cdot - 4 = - 2 j$

Step 1.1.8.2

Factor $2$ out of $6 j$ .

$10 j - 10 + \frac{- 3}{2} (2 (3 j)) - \frac{3}{2} \cdot - 4 = - 2 j$

Step 1.1.8.3

Cancel the common factor.

$10 j - 10 + \frac{- 3}{2} (2 (3 j)) - \frac{3}{2} \cdot - 4 = - 2 j$

Step 1.1.8.4

Rewrite the expression.

$10 j - 10 - 3 (3 j) - \frac{3}{2} \cdot - 4 = - 2 j$

Step 1.1.9

Multiply $3$ by $- 3$ .

$10 j - 10 - 9 j - \frac{3}{2} \cdot - 4 = - 2 j$

Step 1.1.10

Cancel the common factor of $2$ .

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Step 1.1.10.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$10 j - 10 - 9 j + \frac{- 3}{2} \cdot - 4 = - 2 j$

Step 1.1.10.2

Factor $2$ out of $- 4$ .

$10 j - 10 - 9 j + \frac{- 3}{2} \cdot (2 (- 2)) = - 2 j$

Step 1.1.10.3

Cancel the common factor.

$10 j - 10 - 9 j + \frac{- 3}{2} \cdot (2 \cdot - 2) = - 2 j$

Step 1.1.10.4

Rewrite the expression.

$10 j - 10 - 9 j - 3 \cdot - 2 = - 2 j$

Step 1.1.11

Multiply $- 3$ by $- 2$ .

$10 j - 10 - 9 j + 6 = - 2 j$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $9 j$ from $10 j$ .

$j - 10 + 6 = - 2 j$

Step 1.2.2

Add $- 10$ and $6$ .

$j - 4 = - 2 j$

Step 2

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

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Step 2.1

Add $2 j$ to both sides of the equation.

$j - 4 + 2 j = 0$

Step 2.2

Add $j$ and $2 j$ .

$3 j - 4 = 0$

Step 3

Add $4$ to both sides of the equation.

$3 j = 4$

Step 4

Divide each term in $3 j = 4$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 j = 4$ by $3$ .

$\frac{3 j}{3} = \frac{4}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 j}{3} = \frac{4}{3}$

Step 4.2.1.2

Divide $j$ by $1$ .

$j = \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$j = \frac{4}{3}$

Decimal Form:

$j = 1.\overline{3}$

Mixed Number Form:

$j = 1 \frac{1}{3}$