Algebra Examples

\frac{2}{3} b + 5 = 20 - b

$\frac{2}{3} b + 5 = 20 - b$

Step 1

Combine

\frac{2}{3}

$\frac{2}{3}$ and

b

$b$ .

\frac{2 b}{3} + 5 = 20 - b

$\frac{2 b}{3} + 5 = 20 - b$

Step 2

Move all terms containing

b

$b$ to the left side of the equation.

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Step 2.1

Add

b

$b$ to both sides of the equation.

\frac{2 b}{3} + 5 + b = 20

$\frac{2 b}{3} + 5 + b = 20$

Step 2.2

To write

b

$b$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 b}{3} + b \cdot \frac{3}{3} + 5 = 20

$\frac{2 b}{3} + b \cdot \frac{3}{3} + 5 = 20$

Step 2.3

Combine

b

$b$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 b}{3} + \frac{b \cdot 3}{3} + 5 = 20

$\frac{2 b}{3} + \frac{b \cdot 3}{3} + 5 = 20$

Step 2.4

Combine the numerators over the common denominator.

\frac{2 b + b \cdot 3}{3} + 5 = 20

$\frac{2 b + b \cdot 3}{3} + 5 = 20$

Step 2.5

Add

2 b

$2 b$ and

b \cdot 3

$b \cdot 3$ .

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Step 2.5.1

Reorder

b

$b$ and

3

$3$ .

\frac{2 b + 3 \cdot b}{3} + 5 = 20

$\frac{2 b + 3 \cdot b}{3} + 5 = 20$

Step 2.5.2

Add

2 b

$2 b$ and

3 \cdot b

$3 \cdot b$ .

\frac{5 b}{3} + 5 = 20

$\frac{5 b}{3} + 5 = 20$

\frac{5 b}{3} + 5 = 20

$\frac{5 b}{3} + 5 = 20$

\frac{5 b}{3} + 5 = 20

$\frac{5 b}{3} + 5 = 20$

Step 3

Move all terms not containing

b

$b$ to the right side of the equation.

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Step 3.1

Subtract

5

$5$ from both sides of the equation.

\frac{5 b}{3} = 20 - 5

$\frac{5 b}{3} = 20 - 5$

Step 3.2

Subtract

5

$5$ from

20

$20$ .

\frac{5 b}{3} = 15

$\frac{5 b}{3} = 15$

\frac{5 b}{3} = 15

$\frac{5 b}{3} = 15$

Step 4

Multiply both sides of the equation by

\frac{3}{5}

$\frac{3}{5}$ .

\frac{3}{5} \cdot \frac{5 b}{3} = \frac{3}{5} \cdot 15

$\frac{3}{5} \cdot \frac{5 b}{3} = \frac{3}{5} \cdot 15$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify

\frac{3}{5} \cdot \frac{5 b}{3}

$\frac{3}{5} \cdot \frac{5 b}{3}$ .

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Step 5.1.1.1

Cancel the common factor of

3

$3$ .

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Step 5.1.1.1.1

Cancel the common factor.

\frac{3}{5} \cdot \frac{5 b}{3} = \frac{3}{5} \cdot 15

$\frac{3}{5} \cdot \frac{5 b}{3} = \frac{3}{5} \cdot 15$

Step 5.1.1.1.2

Rewrite the expression.

\frac{1}{5} (5 b) = \frac{3}{5} \cdot 15

$\frac{1}{5} (5 b) = \frac{3}{5} \cdot 15$

\frac{1}{5} (5 b) = \frac{3}{5} \cdot 15

$\frac{1}{5} (5 b) = \frac{3}{5} \cdot 15$

Step 5.1.1.2

Cancel the common factor of

5

$5$ .

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Step 5.1.1.2.1

Factor

5

$5$ out of

5 b

$5 b$ .

\frac{1}{5} (5 (b)) = \frac{3}{5} \cdot 15

$\frac{1}{5} (5 (b)) = \frac{3}{5} \cdot 15$

Step 5.1.1.2.2

Cancel the common factor.

\frac{1}{5} (5 b) = \frac{3}{5} \cdot 15

$\frac{1}{5} (5 b) = \frac{3}{5} \cdot 15$

Step 5.1.1.2.3

Rewrite the expression.

b = \frac{3}{5} \cdot 15

$b = \frac{3}{5} \cdot 15$

b = \frac{3}{5} \cdot 15

$b = \frac{3}{5} \cdot 15$

b = \frac{3}{5} \cdot 15

$b = \frac{3}{5} \cdot 15$

b = \frac{3}{5} \cdot 15

$b = \frac{3}{5} \cdot 15$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

\frac{3}{5} \cdot 15

$\frac{3}{5} \cdot 15$ .

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Step 5.2.1.1

Cancel the common factor of

5

$5$ .

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Step 5.2.1.1.1

Factor

5

$5$ out of

15

$15$ .

b = \frac{3}{5} \cdot (5 (3))

$b = \frac{3}{5} \cdot (5 (3))$

Step 5.2.1.1.2

Cancel the common factor.

b = \frac{3}{5} \cdot (5 \cdot 3)

$b = \frac{3}{5} \cdot (5 \cdot 3)$

Step 5.2.1.1.3

Rewrite the expression.

b = 3 \cdot 3

$b = 3 \cdot 3$

b = 3 \cdot 3

$b = 3 \cdot 3$

Step 5.2.1.2

Multiply

3

$3$ by

3

$3$ .

b = 9

$b = 9$

b = 9

$b = 9$

b = 9

$b = 9$

b = 9

$b = 9$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$