Basic Math Examples

\frac{3}{2} b + (b + 45) + 90 + (2 b - 90) + b = 540

$\frac{3}{2} b + (b + 45) + 90 + (2 b - 90) + b = 540$

Step 1

Simplify

\frac{3}{2} b + b + 45 + 90 + 2 b - 90 + b

$\frac{3}{2} b + b + 45 + 90 + 2 b - 90 + b$ .

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Step 1.1

Combine the opposite terms in

\frac{3}{2} b + b + 45 + 90 + 2 b - 90 + b

$\frac{3}{2} b + b + 45 + 90 + 2 b - 90 + b$ .

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Step 1.1.1

Subtract

90

$90$ from

90

$90$ .

\frac{3}{2} b + b + 45 + 2 b + 0 + b = 540

$\frac{3}{2} b + b + 45 + 2 b + 0 + b = 540$

Step 1.1.2

Add

\frac{3}{2} b + b + 45 + 2 b

$\frac{3}{2} b + b + 45 + 2 b$ and

0

$0$ .

\frac{3}{2} b + b + 45 + 2 b + b = 540

$\frac{3}{2} b + b + 45 + 2 b + b = 540$

\frac{3}{2} b + b + 45 + 2 b + b = 540

$\frac{3}{2} b + b + 45 + 2 b + b = 540$

Step 1.2

Combine

\frac{3}{2}

$\frac{3}{2}$ and

b

$b$ .

\frac{3 b}{2} + b + 45 + 2 b + b = 540

$\frac{3 b}{2} + b + 45 + 2 b + b = 540$

Step 1.3

To write

b

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3 b}{2} + b \cdot \frac{2}{2} + 45 + 2 b + b = 540

$\frac{3 b}{2} + b \cdot \frac{2}{2} + 45 + 2 b + b = 540$

Step 1.4

Combine

b

$b$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3 b}{2} + \frac{b \cdot 2}{2} + 45 + 2 b + b = 540

$\frac{3 b}{2} + \frac{b \cdot 2}{2} + 45 + 2 b + b = 540$

Step 1.5

Combine the numerators over the common denominator.

\frac{3 b + b \cdot 2}{2} + 45 + 2 b + b = 540

$\frac{3 b + b \cdot 2}{2} + 45 + 2 b + b = 540$

Step 1.6

Add

3 b

$3 b$ and

b \cdot 2

$b \cdot 2$ .

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Step 1.6.1

Reorder

b

$b$ and

2

$2$ .

\frac{3 b + 2 \cdot b}{2} + 45 + 2 b + b = 540

$\frac{3 b + 2 \cdot b}{2} + 45 + 2 b + b = 540$

Step 1.6.2

Add

3 b

$3 b$ and

2 \cdot b

$2 \cdot b$ .

\frac{5 b}{2} + 45 + 2 b + b = 540

$\frac{5 b}{2} + 45 + 2 b + b = 540$

\frac{5 b}{2} + 45 + 2 b + b = 540

$\frac{5 b}{2} + 45 + 2 b + b = 540$

Step 1.7

To write

2 b

$2 b$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5 b}{2} + 2 b \cdot \frac{2}{2} + 45 + b = 540

$\frac{5 b}{2} + 2 b \cdot \frac{2}{2} + 45 + b = 540$

Step 1.8

Simplify terms.

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Step 1.8.1

Combine

2 b

$2 b$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5 b}{2} + \frac{2 b \cdot 2}{2} + 45 + b = 540

$\frac{5 b}{2} + \frac{2 b \cdot 2}{2} + 45 + b = 540$

Step 1.8.2

Combine the numerators over the common denominator.

\frac{5 b + 2 b \cdot 2}{2} + 45 + b = 540

$\frac{5 b + 2 b \cdot 2}{2} + 45 + b = 540$

\frac{5 b + 2 b \cdot 2}{2} + 45 + b = 540

$\frac{5 b + 2 b \cdot 2}{2} + 45 + b = 540$

Step 1.9

Simplify each term.

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Step 1.9.1

Simplify the numerator.

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Step 1.9.1.1

Factor

b

$b$ out of

5 b + 2 b \cdot 2

$5 b + 2 b \cdot 2$ .

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Step 1.9.1.1.1

Factor

b

$b$ out of

5 b

$5 b$ .

\frac{b \cdot 5 + 2 b \cdot 2}{2} + 45 + b = 540

$\frac{b \cdot 5 + 2 b \cdot 2}{2} + 45 + b = 540$

Step 1.9.1.1.2

Factor

b

$b$ out of

2 b \cdot 2

$2 b \cdot 2$ .

\frac{b \cdot 5 + b (2 \cdot 2)}{2} + 45 + b = 540

$\frac{b \cdot 5 + b (2 \cdot 2)}{2} + 45 + b = 540$

Step 1.9.1.1.3

Factor

$b$ out of

$b \cdot 5 + b (2 \cdot 2)$ .

$\frac{b (5 + 2 \cdot 2)}{2} + 45 + b = 540$

Step 1.9.1.2

Multiply

$2$ by

$2$ .

$\frac{b (5 + 4)}{2} + 45 + b = 540$

Step 1.9.1.3

Add

$5$ and

$4$ .

$\frac{b \cdot 9}{2} + 45 + b = 540$

Step 1.9.2

Move

$9$ to the left of

$b$ .

$\frac{9 b}{2} + 45 + b = 540$

Step 1.10

To write

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

$\frac{2}{2}$ .

$\frac{9 b}{2} + b \cdot \frac{2}{2} + 45 = 540$

Step 1.11

Combine

$b$ and

$\frac{2}{2}$ .

$\frac{9 b}{2} + \frac{b \cdot 2}{2} + 45 = 540$

Step 1.12

Combine the numerators over the common denominator.

$\frac{9 b + b \cdot 2}{2} + 45 = 540$

Step 1.13

Add

$9 b$ and

$b \cdot 2$ .

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Step 1.13.1

Reorder

$b$ and

$2$ .

$\frac{9 b + 2 \cdot b}{2} + 45 = 540$

Step 1.13.2

Add

$9 b$ and

$2 \cdot b$ .

$\frac{11 b}{2} + 45 = 540$

Step 2

Move all terms not containing

$b$ to the right side of the equation.

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Step 2.1

Subtract

$45$ from both sides of the equation.

$\frac{11 b}{2} = 540 - 45$

Step 2.2

Subtract

$45$ from

$540$ .

$\frac{11 b}{2} = 495$

Step 3

Multiply both sides of the equation by

$\frac{2}{11}$ .

$\frac{2}{11} \cdot \frac{11 b}{2} = \frac{2}{11} \cdot 495$

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

$\frac{2}{11} \cdot \frac{11 b}{2}$ .

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Step 4.1.1.1

Cancel the common factor of

$2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{11} \cdot \frac{11 b}{2} = \frac{2}{11} \cdot 495$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 b) = \frac{2}{11} \cdot 495$

Step 4.1.1.2

Cancel the common factor of

$11$ .

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Step 4.1.1.2.1

Factor

$11$ out of

$11 b$ .

$\frac{1}{11} (11 (b)) = \frac{2}{11} \cdot 495$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 b) = \frac{2}{11} \cdot 495$

Step 4.1.1.2.3

Rewrite the expression.

$b = \frac{2}{11} \cdot 495$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify

$\frac{2}{11} \cdot 495$ .

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Step 4.2.1.1

Cancel the common factor of

$11$ .

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Step 4.2.1.1.1

Factor

$11$ out of

$495$ .

$b = \frac{2}{11} \cdot (11 (45))$

Step 4.2.1.1.2

Cancel the common factor.

$b = \frac{2}{11} \cdot (11 \cdot 45)$

Step 4.2.1.1.3

Rewrite the expression.

$b = 2 \cdot 45$

Step 4.2.1.2

Multiply

$2$ by

$45$ .

$b = 90$