Solve for x x+7-7/6=(2x+7)/30

$x + 7 - \frac{7}{6} = \frac{2 x + 7}{30}$

Step 1

Multiply both sides by $30$ .

$(x + 7 - \frac{7}{6}) \cdot 30 = \frac{2 x + 7}{30} \cdot 30$

Step 2

Simplify.

Simplify the left side.

Simplify $(x + 7 - \frac{7}{6}) \cdot 30$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(x + 7 \cdot \frac{6}{6} - \frac{7}{6}) \cdot 30 = \frac{2 x + 7}{30} \cdot 30$

Combine $7$ and $\frac{6}{6}$ .

$(x + \frac{7 \cdot 6}{6} - \frac{7}{6}) \cdot 30 = \frac{2 x + 7}{30} \cdot 30$

Combine the numerators over the common denominator.

$(x + \frac{7 \cdot 6 - 7}{6}) \cdot 30 = \frac{2 x + 7}{30} \cdot 30$

Simplify the numerator.

Multiply $7$ by $6$ .

$(x + \frac{42 - 7}{6}) \cdot 30 = \frac{2 x + 7}{30} \cdot 30$

Subtract $7$ from $42$ .

$(x + \frac{35}{6}) \cdot 30 = \frac{2 x + 7}{30} \cdot 30$

Apply the distributive property.

$x \cdot 30 + \frac{35}{6} \cdot 30 = \frac{2 x + 7}{30} \cdot 30$

Move $30$ to the left of $x$ .

$30 \cdot x + \frac{35}{6} \cdot 30 = \frac{2 x + 7}{30} \cdot 30$

Cancel the common factor of $6$ .

Factor $6$ out of $30$ .

$30 \cdot x + \frac{35}{6} \cdot (6 (5)) = \frac{2 x + 7}{30} \cdot 30$

Cancel the common factor.

$30 \cdot x + \frac{35}{6} \cdot (6 \cdot 5) = \frac{2 x + 7}{30} \cdot 30$

Rewrite the expression.

$30 \cdot x + 35 \cdot 5 = \frac{2 x + 7}{30} \cdot 30$

Multiply $35$ by $5$ .

$30 x + 175 = \frac{2 x + 7}{30} \cdot 30$

Simplify the right side.

Cancel the common factor of $30$ .

Cancel the common factor.

$30 x + 175 = \frac{2 x + 7}{30} \cdot 30$

Rewrite the expression.

$30 x + 175 = 2 x + 7$

Step 3

Solve for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$30 x + 175 - 2 x = 7$

Subtract $2 x$ from $30 x$ .

$28 x + 175 = 7$

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

Subtract $175$ from both sides of the equation.

$28 x = 7 - 175$

Subtract $175$ from $7$ .

$28 x = - 168$

Divide each term in $28 x = - 168$ by $28$ and simplify.

Divide each term in $28 x = - 168$ by $28$ .

$\frac{28 x}{28} = \frac{- 168}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 x}{28} = \frac{- 168}{28}$

Divide $x$ by $1$ .

$x = \frac{- 168}{28}$

Simplify the right side.

Divide $- 168$ by $28$ .

$x = - 6$

Solve for x x+7-7/6=(2x+7)/30

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