Basic Math Examples

$\frac{0.4 N - 1}{7} = 5$

Step 1

Multiply both sides by $7$ .

$\frac{0.4 N - 1}{7} \cdot 7 = 5 \cdot 7$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{0.4 N - 1}{7} \cdot 7$ .

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Step 2.1.1.1

Factor $0.2$ out of $0.4 N - 1$ .

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Step 2.1.1.1.1

Factor $0.2$ out of $0.4 N$ .

$\frac{0.2 (2 N) - 1}{7} \cdot 7 = 5 \cdot 7$

Step 2.1.1.1.2

Factor $0.2$ out of $- 1$ .

$\frac{0.2 (2 N) + 0.2 (- 5)}{7} \cdot 7 = 5 \cdot 7$

Step 2.1.1.1.3

Factor $0.2$ out of $0.2 (2 N) + 0.2 (- 5)$ .

$\frac{0.2 (2 N - 5)}{7} \cdot 7 = 5 \cdot 7$

Step 2.1.1.2

Cancel the common factor of $0.2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{0.2 (2 N - 5)}{7} \cdot 7 = 5 \cdot 7$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{2 N - 5}{7} \cdot \frac{7}{5} = 5 \cdot 7$

Step 2.1.1.3

Cancel the common factor of $7$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{2 N - 5}{7} \cdot \frac{7}{5} = 5 \cdot 7$

Step 2.1.1.3.2

Rewrite the expression.

$(2 N - 5) \cdot \frac{1}{5} = 5 \cdot 7$

Step 2.1.1.4

Apply the distributive property.

$2 N \frac{1}{5} - 5 (\frac{1}{5}) = 5 \cdot 7$

Step 2.1.1.5

Multiply $2 N \frac{1}{5}$ .

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Step 2.1.1.5.1

Combine $2$ and $\frac{1}{5}$ .

$N \frac{2}{5} - 5 (\frac{1}{5}) = 5 \cdot 7$

Step 2.1.1.5.2

Combine $N$ and $\frac{2}{5}$ .

$\frac{N \cdot 2}{5} - 5 (\frac{1}{5}) = 5 \cdot 7$

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Factor $5$ out of $- 5$ .

$\frac{N \cdot 2}{5} + 5 (- 1) \frac{1}{5} = 5 \cdot 7$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{N \cdot 2}{5} + 5 \cdot - 1 \frac{1}{5} = 5 \cdot 7$

Step 2.1.1.6.3

Rewrite the expression.

$\frac{N \cdot 2}{5} - 1 = 5 \cdot 7$

Step 2.1.1.7

Move $2$ to the left of $N$ .

$\frac{2 N}{5} - 1 = 5 \cdot 7$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $7$ .

$\frac{2 N}{5} - 1 = 35$

Step 3

Solve for $N$ .

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Step 3.1

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

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Step 3.1.1

Add $1$ to both sides of the equation.

$\frac{2 N}{5} = 35 + 1$

Step 3.1.2

Add $35$ and $1$ .

$\frac{2 N}{5} = 36$

Step 3.2

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 N}{5} = \frac{5}{2} \cdot 36$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{5}{2} \cdot \frac{2 N}{5}$ .

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Step 3.3.1.1.1

Cancel the common factor of $5$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 N}{5} = \frac{5}{2} \cdot 36$

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 N) = \frac{5}{2} \cdot 36$

Step 3.3.1.1.2

Cancel the common factor of $2$ .

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Step 3.3.1.1.2.1

Factor $2$ out of $2 N$ .

$\frac{1}{2} (2 (N)) = \frac{5}{2} \cdot 36$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 N) = \frac{5}{2} \cdot 36$

Step 3.3.1.1.2.3

Rewrite the expression.

$N = \frac{5}{2} \cdot 36$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{5}{2} \cdot 36$ .

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Step 3.3.2.1.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1.1

Factor $2$ out of $36$ .

$N = \frac{5}{2} \cdot (2 (18))$

Step 3.3.2.1.1.2

Cancel the common factor.

$N = \frac{5}{2} \cdot (2 \cdot 18)$

Step 3.3.2.1.1.3

Rewrite the expression.

$N = 5 \cdot 18$

Step 3.3.2.1.2

Multiply $5$ by $18$ .

$N = 90$