Algebra Examples

$7 (2 m - 1) - \frac{3}{5} m = \frac{6}{5} (4 - 3 m)$

Step 1

Simplify $7 (2 m - 1) - \frac{3}{5} m$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$7 (2 m) + 7 \cdot - 1 - \frac{3}{5} m = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.1.2

Multiply $2$ by $7$ .

$14 m + 7 \cdot - 1 - \frac{3}{5} m = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.1.3

Multiply $7$ by $- 1$ .

$14 m - 7 - \frac{3}{5} m = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.1.4

Combine $m$ and $\frac{3}{5}$ .

$14 m - 7 - \frac{m \cdot 3}{5} = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.1.5

Move $3$ to the left of $m$ .

$14 m - 7 - \frac{3 m}{5} = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.2

To write $14 m$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$14 m \cdot \frac{5}{5} - \frac{3 m}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $14 m$ and $\frac{5}{5}$ .

$\frac{14 m \cdot 5}{5} - \frac{3 m}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{14 m \cdot 5 - 3 m}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $m$ out of $14 m \cdot 5 - 3 m$ .

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Step 1.4.1.1.1

Factor $m$ out of $14 m \cdot 5$ .

$\frac{m (14 \cdot 5) - 3 m}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.4.1.1.2

Factor $m$ out of $- 3 m$ .

$\frac{m (14 \cdot 5) + m \cdot - 3}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.4.1.1.3

Factor $m$ out of $m (14 \cdot 5) + m \cdot - 3$ .

$\frac{m (14 \cdot 5 - 3)}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.4.1.2

Multiply $14$ by $5$ .

$\frac{m (70 - 3)}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.4.1.3

Subtract $3$ from $70$ .

$\frac{m \cdot 67}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 1.4.2

Move $67$ to the left of $m$ .

$\frac{67 m}{5} - 7 = \frac{6}{5} \cdot (4 - 3 m)$

Step 2

Simplify $\frac{6}{5} \cdot (4 - 3 m)$ .

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Step 2.1

Apply the distributive property.

$\frac{67 m}{5} - 7 = \frac{6}{5} \cdot 4 + \frac{6}{5} (- 3 m)$

Step 2.2

Multiply $\frac{6}{5} \cdot 4$ .

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Step 2.2.1

Combine $\frac{6}{5}$ and $4$ .

$\frac{67 m}{5} - 7 = \frac{6 \cdot 4}{5} + \frac{6}{5} (- 3 m)$

Step 2.2.2

Multiply $6$ by $4$ .

$\frac{67 m}{5} - 7 = \frac{24}{5} + \frac{6}{5} (- 3 m)$

Step 2.3

Multiply $\frac{6}{5} (- 3 m)$ .

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Step 2.3.1

Combine $- 3$ and $\frac{6}{5}$ .

$\frac{67 m}{5} - 7 = \frac{24}{5} + \frac{- 3 \cdot 6}{5} m$

Step 2.3.2

Multiply $- 3$ by $6$ .

$\frac{67 m}{5} - 7 = \frac{24}{5} + \frac{- 18}{5} m$

Step 2.3.3

Combine $\frac{- 18}{5}$ and $m$ .

$\frac{67 m}{5} - 7 = \frac{24}{5} + \frac{- 18 m}{5}$

Step 2.4

Move the negative in front of the fraction.

$\frac{67 m}{5} - 7 = \frac{24}{5} - \frac{18 m}{5}$

Step 3

Move all terms containing $m$ to the left side of the equation.

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Step 3.1

Add $\frac{18 m}{5}$ to both sides of the equation.

$\frac{67 m}{5} - 7 + \frac{18 m}{5} = \frac{24}{5}$

Step 3.2

Combine the numerators over the common denominator.

$- 7 + \frac{67 m + 18 m}{5} = \frac{24}{5}$

Step 3.3

Add $67 m$ and $18 m$ .

$- 7 + \frac{85 m}{5} = \frac{24}{5}$

Step 3.4

Cancel the common factor of $85$ and $5$ .

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Step 3.4.1

Factor $5$ out of $85 m$ .

$- 7 + \frac{5 (17 m)}{5} = \frac{24}{5}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $5$ out of $5$ .

$- 7 + \frac{5 (17 m)}{5 (1)} = \frac{24}{5}$

Step 3.4.2.2

Cancel the common factor.

$- 7 + \frac{5 (17 m)}{5 \cdot 1} = \frac{24}{5}$

Step 3.4.2.3

Rewrite the expression.

$- 7 + \frac{17 m}{1} = \frac{24}{5}$

Step 3.4.2.4

Divide $17 m$ by $1$ .

$- 7 + 17 m = \frac{24}{5}$

Step 4

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

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Step 4.1

Add $7$ to both sides of the equation.

$17 m = \frac{24}{5} + 7$

Step 4.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$17 m = \frac{24}{5} + 7 \cdot \frac{5}{5}$

Step 4.3

Combine $7$ and $\frac{5}{5}$ .

$17 m = \frac{24}{5} + \frac{7 \cdot 5}{5}$

Step 4.4

Combine the numerators over the common denominator.

$17 m = \frac{24 + 7 \cdot 5}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $7$ by $5$ .

$17 m = \frac{24 + 35}{5}$

Step 4.5.2

Add $24$ and $35$ .

$17 m = \frac{59}{5}$

Step 5

Divide each term in $17 m = \frac{59}{5}$ by $17$ and simplify.

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Step 5.1

Divide each term in $17 m = \frac{59}{5}$ by $17$ .

$\frac{17 m}{17} = \frac{\frac{59}{5}}{17}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $17$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{17 m}{17} = \frac{\frac{59}{5}}{17}$

Step 5.2.1.2

Divide $m$ by $1$ .

$m = \frac{\frac{59}{5}}{17}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$m = \frac{59}{5} \cdot \frac{1}{17}$

Step 5.3.2

Multiply $\frac{59}{5} \cdot \frac{1}{17}$ .

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Step 5.3.2.1

Multiply $\frac{59}{5}$ by $\frac{1}{17}$ .

$m = \frac{59}{5 \cdot 17}$

Step 5.3.2.2

Multiply $5$ by $17$ .

$m = \frac{59}{85}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{59}{85}$

Decimal Form:

$m = 0.69411764 \dots$