Basic Math Examples

$\frac{7 d - 3}{4} + \frac{5 (2 d - 9)}{7} + 4 = 21$

Step 1

Simplify $\frac{7 d - 3}{4} + \frac{5 (2 d - 9)}{7} + 4$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{7 d - 3}{4}$ by $\frac{7}{7}$ .

$\frac{7 d - 3}{4} \cdot \frac{7}{7} + \frac{5 (2 d - 9)}{7} + 4 = 21$

Step 1.1.2

Multiply $\frac{7 d - 3}{4}$ by $\frac{7}{7}$ .

$\frac{(7 d - 3) \cdot 7}{4 \cdot 7} + \frac{5 (2 d - 9)}{7} + 4 = 21$

Step 1.1.3

Multiply $\frac{5 (2 d - 9)}{7}$ by $\frac{4}{4}$ .

$\frac{(7 d - 3) \cdot 7}{4 \cdot 7} + \frac{5 (2 d - 9)}{7} \cdot \frac{4}{4} + 4 = 21$

Step 1.1.4

Multiply $\frac{5 (2 d - 9)}{7}$ by $\frac{4}{4}$ .

$\frac{(7 d - 3) \cdot 7}{4 \cdot 7} + \frac{5 (2 d - 9) \cdot 4}{7 \cdot 4} + 4 = 21$

Step 1.1.5

Write $4$ as a fraction with denominator $1$ .

$\frac{(7 d - 3) \cdot 7}{4 \cdot 7} + \frac{5 (2 d - 9) \cdot 4}{7 \cdot 4} + \frac{4}{1} = 21$

Step 1.1.6

Multiply $\frac{4}{1}$ by $\frac{28}{28}$ .

$\frac{(7 d - 3) \cdot 7}{4 \cdot 7} + \frac{5 (2 d - 9) \cdot 4}{7 \cdot 4} + \frac{4}{1} \cdot \frac{28}{28} = 21$

Step 1.1.7

Multiply $\frac{4}{1}$ by $\frac{28}{28}$ .

$\frac{(7 d - 3) \cdot 7}{4 \cdot 7} + \frac{5 (2 d - 9) \cdot 4}{7 \cdot 4} + \frac{4 \cdot 28}{28} = 21$

Step 1.1.8

Multiply $4$ by $7$ .

$\frac{(7 d - 3) \cdot 7}{28} + \frac{5 (2 d - 9) \cdot 4}{7 \cdot 4} + \frac{4 \cdot 28}{28} = 21$

Step 1.1.9

Reorder the factors of $7 \cdot 4$ .

$\frac{(7 d - 3) \cdot 7}{28} + \frac{5 (2 d - 9) \cdot 4}{4 \cdot 7} + \frac{4 \cdot 28}{28} = 21$

Step 1.1.10

Multiply $4$ by $7$ .

$\frac{(7 d - 3) \cdot 7}{28} + \frac{5 (2 d - 9) \cdot 4}{28} + \frac{4 \cdot 28}{28} = 21$

Step 1.2

Combine the numerators over the common denominator.

$\frac{(7 d - 3) \cdot 7 + 5 (2 d - 9) \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{7 d \cdot 7 - 3 \cdot 7 + 5 (2 d - 9) \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3.2

Multiply $7$ by $7$ .

$\frac{49 d - 3 \cdot 7 + 5 (2 d - 9) \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3.3

Multiply $- 3$ by $7$ .

$\frac{49 d - 21 + 5 (2 d - 9) \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3.4

Apply the distributive property.

$\frac{49 d - 21 + (5 (2 d) + 5 \cdot - 9) \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3.5

Multiply $2$ by $5$ .

$\frac{49 d - 21 + (10 d + 5 \cdot - 9) \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3.6

Multiply $5$ by $- 9$ .

$\frac{49 d - 21 + (10 d - 45) \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3.7

Apply the distributive property.

$\frac{49 d - 21 + 10 d \cdot 4 - 45 \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3.8

Multiply $4$ by $10$ .

$\frac{49 d - 21 + 40 d - 45 \cdot 4 + 4 \cdot 28}{28} = 21$

Step 1.3.9

Multiply $- 45$ by $4$ .

$\frac{49 d - 21 + 40 d - 180 + 4 \cdot 28}{28} = 21$

Step 1.3.10

Multiply $4$ by $28$ .

$\frac{49 d - 21 + 40 d - 180 + 112}{28} = 21$

Step 1.4

Simplify terms.

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Step 1.4.1

Add $49 d$ and $40 d$ .

$\frac{89 d - 21 - 180 + 112}{28} = 21$

Step 1.4.2

Simplify by adding and subtracting.

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Step 1.4.2.1

Subtract $180$ from $- 21$ .

$\frac{89 d - 201 + 112}{28} = 21$

Step 1.4.2.2

Add $- 201$ and $112$ .

$\frac{89 d - 89}{28} = 21$

Step 1.4.3

Factor $89$ out of $89 d - 89$ .

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Step 1.4.3.1

Factor $89$ out of $89 d$ .

$\frac{89 (d) - 89}{28} = 21$

Step 1.4.3.2

Factor $89$ out of $- 89$ .

$\frac{89 (d) + 89 (- 1)}{28} = 21$

Step 1.4.3.3

Factor $89$ out of $89 (d) + 89 (- 1)$ .

$\frac{89 (d - 1)}{28} = 21$

Step 2

Multiply both sides of the equation by $\frac{28}{89}$ .

$\frac{28}{89} \cdot \frac{89 (d - 1)}{28} = \frac{28}{89} \cdot 21$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{28}{89} \cdot \frac{89 (d - 1)}{28}$ .

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Step 3.1.1.1

Cancel the common factor of $28$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{28}{89} \cdot \frac{89 (d - 1)}{28} = \frac{28}{89} \cdot 21$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{89} (89 (d - 1)) = \frac{28}{89} \cdot 21$

Step 3.1.1.2

Cancel the common factor of $89$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{1}{89} (89 (d - 1)) = \frac{28}{89} \cdot 21$

Step 3.1.1.2.2

Rewrite the expression.

$d - 1 = \frac{28}{89} \cdot 21$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{28}{89} \cdot 21$ .

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Step 3.2.1.1

Combine $\frac{28}{89}$ and $21$ .

$d - 1 = \frac{28 \cdot 21}{89}$

Step 3.2.1.2

Multiply $28$ by $21$ .

$d - 1 = \frac{588}{89}$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$d = \frac{588}{89} + 1$

Step 4.2

Write $1$ as a fraction with a common denominator.

$d = \frac{588}{89} + \frac{89}{89}$

Step 4.3

Combine the numerators over the common denominator.

$d = \frac{588 + 89}{89}$

Step 4.4

Add $588$ and $89$ .

$d = \frac{677}{89}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = \frac{677}{89}$

Decimal Form:

$d = 7.60674157 \dots$

Mixed Number Form:

$d = 7 \frac{54}{89}$