Algebra Examples

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

Step 1

Multiply both sides by $4$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{- 5}{7} \cdot 4$ .

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Step 2.2.1.1

Move the negative in front of the fraction.

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

Step 2.2.1.2

Multiply $- \frac{5}{7} \cdot 4$ .

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Step 2.2.1.2.1

Multiply $4$ by $- 1$ .

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

Step 2.2.1.2.2

Combine $- 4$ and $\frac{5}{7}$ .

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

Step 2.2.1.2.3

Multiply $- 4$ by $5$ .

$3 x - 5 = \frac{- 20}{7}$

Step 2.2.1.3

Move the negative in front of the fraction.

$3 x - 5 = - \frac{20}{7}$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $5$ to both sides of the equation.

$3 x = - \frac{20}{7} + 5$

Step 3.1.2

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

$3 x = - \frac{20}{7} + 5 \cdot \frac{7}{7}$

Step 3.1.3

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

$3 x = - \frac{20}{7} + \frac{5 \cdot 7}{7}$

Step 3.1.4

Combine the numerators over the common denominator.

$3 x = \frac{- 20 + 5 \cdot 7}{7}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $5$ by $7$ .

$3 x = \frac{- 20 + 35}{7}$

Step 3.1.5.2

Add $- 20$ and $35$ .

$3 x = \frac{15}{7}$

Step 3.2

Divide each term in $3 x = \frac{15}{7}$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x = \frac{15}{7}$ by $3$ .

$\frac{3 x}{3} = \frac{\frac{15}{7}}{3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\frac{15}{7}}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{15}{7}}{3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{15}{7} \cdot \frac{1}{3}$

Step 3.2.3.2

Cancel the common factor of $3$ .

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Step 3.2.3.2.1

Factor $3$ out of $15$ .

$x = \frac{3 (5)}{7} \cdot \frac{1}{3}$

Step 3.2.3.2.2

Cancel the common factor.

$x = \frac{3 \cdot 5}{7} \cdot \frac{1}{3}$

Step 3.2.3.2.3

Rewrite the expression.

$x = \frac{5}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{7}$

Decimal Form:

$x = 0.\overline{714285}$