Basic Math Examples

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

Step 1

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

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Step 1.1

Combine the opposite terms in $\frac{3}{2} b + b + 45 + 90 + 2 b - 90 + b$ .

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Step 1.1.1

Subtract $90$ from $90$ .

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

Step 1.1.2

Add $\frac{3}{2} b + b + 45 + 2 b$ and $0$ .

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

Step 1.2

Combine $\frac{3}{2}$ and $b$ .

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

Step 1.3

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

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

Step 1.4

Combine $b$ and $\frac{2}{2}$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Add $3 b$ and $b \cdot 2$ .

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Step 1.6.1

Reorder $b$ and $2$ .

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

Step 1.6.2

Add $3 b$ and $2 \cdot b$ .

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

Step 1.7

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

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

Step 1.8

Simplify terms.

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Step 1.8.1

Combine $2 b$ and $\frac{2}{2}$ .

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

Step 1.8.2

Combine the numerators over the common denominator.

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

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 $b$ out of $5 b + 2 b \cdot 2$ .

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Step 1.9.1.1.1

Factor $b$ out of $5 b$ .

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

Step 1.9.1.1.2

Factor $b$ out of $2 b \cdot 2$ .

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

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 $45$ .

$b = 90$