Pre-Algebra Examples

$7 x + \frac{5 y}{6} = 6$

Step 1

Subtract $\frac{5 y}{6}$ from both sides of the equation.

$7 x = 6 - \frac{5 y}{6}$

Step 2

Divide each term in $7 x = 6 - \frac{5 y}{6}$ by $7$ and simplify.

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Step 2.1

Divide each term in $7 x = 6 - \frac{5 y}{6}$ by $7$ .

$\frac{7 x}{7} = \frac{6}{7} + \frac{- \frac{5 y}{6}}{7}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{6}{7} + \frac{- \frac{5 y}{6}}{7}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{7} + \frac{- \frac{5 y}{6}}{7}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{6}{7} - \frac{5 y}{6} \cdot \frac{1}{7}$

Step 2.3.1.2

Multiply $- \frac{5 y}{6} \cdot \frac{1}{7}$ .

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Step 2.3.1.2.1

Multiply $\frac{1}{7}$ by $\frac{5 y}{6}$ .

$x = \frac{6}{7} - \frac{5 y}{7 \cdot 6}$

Step 2.3.1.2.2

Multiply $7$ by $6$ .

$x = \frac{6}{7} - \frac{5 y}{42}$