Pre-Algebra Examples

$- 5 x + \frac{4}{7} = \frac{3}{5}$

Step 1

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

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Step 1.1

Subtract $\frac{4}{7}$ from both sides of the equation.

$- 5 x = \frac{3}{5} - \frac{4}{7}$

Step 1.2

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- 5 x = \frac{3}{5} \cdot \frac{7}{7} - \frac{4}{7}$

Step 1.3

To write $- \frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 5 x = \frac{3}{5} \cdot \frac{7}{7} - \frac{4}{7} \cdot \frac{5}{5}$

Step 1.4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3}{5}$ by $\frac{7}{7}$ .

$- 5 x = \frac{3 \cdot 7}{5 \cdot 7} - \frac{4}{7} \cdot \frac{5}{5}$

Step 1.4.2

Multiply $5$ by $7$ .

$- 5 x = \frac{3 \cdot 7}{35} - \frac{4}{7} \cdot \frac{5}{5}$

Step 1.4.3

Multiply $\frac{4}{7}$ by $\frac{5}{5}$ .

$- 5 x = \frac{3 \cdot 7}{35} - \frac{4 \cdot 5}{7 \cdot 5}$

Step 1.4.4

Multiply $7$ by $5$ .

$- 5 x = \frac{3 \cdot 7}{35} - \frac{4 \cdot 5}{35}$

Step 1.5

Combine the numerators over the common denominator.

$- 5 x = \frac{3 \cdot 7 - 4 \cdot 5}{35}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $3$ by $7$ .

$- 5 x = \frac{21 - 4 \cdot 5}{35}$

Step 1.6.2

Multiply $- 4$ by $5$ .

$- 5 x = \frac{21 - 20}{35}$

Step 1.6.3

Subtract $20$ from $21$ .

$- 5 x = \frac{1}{35}$

Step 2

Divide each term in $- 5 x = \frac{1}{35}$ by $- 5$ and simplify.

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Step 2.1

Divide each term in $- 5 x = \frac{1}{35}$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{\frac{1}{35}}{- 5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{\frac{1}{35}}{- 5}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{35}}{- 5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{35} \cdot \frac{1}{- 5}$

Step 2.3.2

Move the negative in front of the fraction.

$x = \frac{1}{35} (- \frac{1}{5})$

Step 2.3.3

Multiply $\frac{1}{35} (- \frac{1}{5})$ .

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Step 2.3.3.1

Multiply $\frac{1}{35}$ by $\frac{1}{5}$ .

$x = - \frac{1}{35 \cdot 5}$

Step 2.3.3.2

Multiply $35$ by $5$ .

$x = - \frac{1}{175}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{175}$

Decimal Form:

$x = - 0.00571428 \dots$