Basic Math Examples

$\frac{1}{5} \cdot (4 d - 1) = 7$

Step 1

Multiply both sides of the equation by $5$ .

$5 (\frac{1}{5} \cdot (4 d - 1)) = 5 \cdot 7$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $5 (\frac{1}{5} \cdot (4 d - 1))$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Multiply $\frac{1}{5} (4 d)$ .

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Step 2.1.1.2.1

Combine $4$ and $\frac{1}{5}$ .

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

Step 2.1.1.2.2

Combine $\frac{4}{5}$ and $d$ .

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

Step 2.1.1.3

Combine $\frac{1}{5}$ and $- 1$ .

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

Step 2.1.1.4

Move the negative in front of the fraction.

$5 (\frac{4 d}{5} - \frac{1}{5}) = 5 \cdot 7$

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Cancel the common factor.

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

Step 2.1.1.6.2

Rewrite the expression.

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

Step 2.1.1.7

Cancel the common factor of $5$ .

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Step 2.1.1.7.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

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

Step 2.1.1.7.2

Cancel the common factor.

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

Step 2.1.1.7.3

Rewrite the expression.

$4 d - 1 = 5 \cdot 7$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $7$ .

$4 d - 1 = 35$

Step 3

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

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Step 3.1

Add $1$ to both sides of the equation.

$4 d = 35 + 1$

Step 3.2

Add $35$ and $1$ .

$4 d = 36$

Step 4

Divide each term in $4 d = 36$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 d = 36$ by $4$ .

$\frac{4 d}{4} = \frac{36}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 d}{4} = \frac{36}{4}$

Step 4.2.1.2

Divide $d$ by $1$ .

$d = \frac{36}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $36$ by $4$ .

$d = 9$