Basic Math Examples

4.75 = \frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67}

$4.75 = \frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67}$

Step 1

Rewrite the equation as

\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} = 4.75

$\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} = 4.75$ .

\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} = 4.75

$\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} = 4.75$

Step 2

Multiply both sides by

21 + 67

$21 + 67$ .

\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67) = 4.75 (21 + 67)

$\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67) = 4.75 (21 + 67)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify

\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67)

$\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67)$ .

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Step 3.1.1.1

Cancel the common factor of

21 + 67

$21 + 67$ .

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Step 3.1.1.1.1

Cancel the common factor.

\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67) = 4.75 (21 + 67)

$\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67) = 4.75 (21 + 67)$

Step 3.1.1.1.2

Rewrite the expression.

21 \cdot (d + 2.25) + 67 \cdot d = 4.75 (21 + 67)

$21 \cdot (d + 2.25) + 67 \cdot d = 4.75 (21 + 67)$

21 \cdot (d + 2.25) + 67 \cdot d = 4.75 (21 + 67)

$21 \cdot (d + 2.25) + 67 \cdot d = 4.75 (21 + 67)$

Step 3.1.1.2

Simplify each term.

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Step 3.1.1.2.1

Apply the distributive property.

21 d + 21 \cdot 2.25 + 67 \cdot d = 4.75 (21 + 67)

$21 d + 21 \cdot 2.25 + 67 \cdot d = 4.75 (21 + 67)$

Step 3.1.1.2.2

Multiply

21

$21$ by

2.25

$2.25$ .

21 d + 47.25 + 67 d = 4.75 (21 + 67)

$21 d + 47.25 + 67 d = 4.75 (21 + 67)$

21 d + 47.25 + 67 d = 4.75 (21 + 67)

$21 d + 47.25 + 67 d = 4.75 (21 + 67)$

Step 3.1.1.3

Add

21 d

$21 d$ and

67 d

$67 d$ .

88 d + 47.25 = 4.75 (21 + 67)

$88 d + 47.25 = 4.75 (21 + 67)$

88 d + 47.25 = 4.75 (21 + 67)

$88 d + 47.25 = 4.75 (21 + 67)$

88 d + 47.25 = 4.75 (21 + 67)

$88 d + 47.25 = 4.75 (21 + 67)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify

4.75 (21 + 67)

$4.75 (21 + 67)$ .

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Step 3.2.1.1

Add

21

$21$ and

67

$67$ .

88 d + 47.25 = 4.75 \cdot 88

$88 d + 47.25 = 4.75 \cdot 88$

Step 3.2.1.2

Multiply

4.75

$4.75$ by

88

$88$ .

88 d + 47.25 = 418

$88 d + 47.25 = 418$

88 d + 47.25 = 418

$88 d + 47.25 = 418$

88 d + 47.25 = 418

$88 d + 47.25 = 418$

88 d + 47.25 = 418

$88 d + 47.25 = 418$

Step 4

Solve for

d

$d$ .

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Step 4.1

Move all terms not containing

d

$d$ to the right side of the equation.

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Step 4.1.1

Subtract

47.25

$47.25$ from both sides of the equation.

88 d = 418 - 47.25

$88 d = 418 - 47.25$

Step 4.1.2

Subtract

47.25

$47.25$ from

418

$418$ .

88 d = 370.75

$88 d = 370.75$

88 d = 370.75

$88 d = 370.75$

Step 4.2

Divide each term in

88 d = 370.75

$88 d = 370.75$ by

88

$88$ and simplify.

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Step 4.2.1

Divide each term in

88 d = 370.75

$88 d = 370.75$ by

88

$88$ .

\frac{88 d}{88} = \frac{370.75}{88}

$\frac{88 d}{88} = \frac{370.75}{88}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

88

$88$ .

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Step 4.2.2.1.1

Cancel the common factor.

\frac{88 d}{88} = \frac{370.75}{88}

$\frac{88 d}{88} = \frac{370.75}{88}$

Step 4.2.2.1.2

Divide

d

$d$ by

1

$1$ .

d = \frac{370.75}{88}

$d = \frac{370.75}{88}$

d = \frac{370.75}{88}

$d = \frac{370.75}{88}$

d = \frac{370.75}{88}

$d = \frac{370.75}{88}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide

370.75

$370.75$ by

88

$88$ .

d = 4.21306 ¯ ¯¯ ¯ 81

$d = 4.21306\overline{81}$

d = 4.21306 ¯ ¯¯ ¯ 81

$d = 4.21306\overline{81}$

d = 4.21306 ¯ ¯¯ ¯ 81

$d = 4.21306\overline{81}$

d = 4.21306 ¯ ¯¯ ¯ 81

$d = 4.21306\overline{81}$