Solve for x (x-1)/4+(2x+7)/9=3x-2

$\frac{x - 1}{4} + \frac{2 x + 7}{9} = 3 x - 2$

Simplify $\frac{x - 1}{4} + \frac{2 x + 7}{9}$ .

To write $\frac{x - 1}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{x - 1}{4} \cdot \frac{9}{9} + \frac{2 x + 7}{9} = 3 x - 2$

To write $\frac{2 x + 7}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x - 1}{4} \cdot \frac{9}{9} + \frac{2 x + 7}{9} \cdot \frac{4}{4} = 3 x - 2$

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x - 1}{4}$ by $\frac{9}{9}$ .

$\frac{(x - 1) \cdot 9}{4 \cdot 9} + \frac{2 x + 7}{9} \cdot \frac{4}{4} = 3 x - 2$

Multiply $4$ by $9$ .

$\frac{(x - 1) \cdot 9}{36} + \frac{2 x + 7}{9} \cdot \frac{4}{4} = 3 x - 2$

Multiply $\frac{2 x + 7}{9}$ by $\frac{4}{4}$ .

$\frac{(x - 1) \cdot 9}{36} + \frac{(2 x + 7) \cdot 4}{9 \cdot 4} = 3 x - 2$

Multiply $9$ by $4$ .

$\frac{(x - 1) \cdot 9}{36} + \frac{(2 x + 7) \cdot 4}{36} = 3 x - 2$

Combine the numerators over the common denominator.

$\frac{(x - 1) \cdot 9 + (2 x + 7) \cdot 4}{36} = 3 x - 2$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 9 - 1 \cdot 9 + (2 x + 7) \cdot 4}{36} = 3 x - 2$

Move $9$ to the left of $x$ .

$\frac{9 \cdot x - 1 \cdot 9 + (2 x + 7) \cdot 4}{36} = 3 x - 2$

Multiply $- 1$ by $9$ .

$\frac{9 \cdot x - 9 + (2 x + 7) \cdot 4}{36} = 3 x - 2$

Apply the distributive property.

$\frac{9 x - 9 + 2 x \cdot 4 + 7 \cdot 4}{36} = 3 x - 2$

Multiply $4$ by $2$ .

$\frac{9 x - 9 + 8 x + 7 \cdot 4}{36} = 3 x - 2$

Multiply $7$ by $4$ .

$\frac{9 x - 9 + 8 x + 28}{36} = 3 x - 2$

Add $9 x$ and $8 x$ .

$\frac{17 x - 9 + 28}{36} = 3 x - 2$

Add $- 9$ and $28$ .

$\frac{17 x + 19}{36} = 3 x - 2$

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

Subtract $3 x$ from both sides of the equation.

$\frac{17 x + 19}{36} - 3 x = - 2$

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{36}{36}$ .

$\frac{17 x + 19}{36} - 3 x \cdot \frac{36}{36} = - 2$

Combine $- 3 x$ and $\frac{36}{36}$ .

$\frac{17 x + 19}{36} + \frac{- 3 x \cdot 36}{36} = - 2$

Combine the numerators over the common denominator.

$\frac{17 x + 19 - 3 x \cdot 36}{36} = - 2$

Simplify the numerator.

Multiply $36$ by $- 3$ .

$\frac{17 x + 19 - 108 x}{36} = - 2$

Subtract $108 x$ from $17 x$ .

$\frac{- 91 x + 19}{36} = - 2$

Factor $- 1$ out of $- 91 x$ .

$\frac{- (91 x) + 19}{36} = - 2$

Rewrite $19$ as $- 1 (- 19)$ .

$\frac{- (91 x) - 1 (- 19)}{36} = - 2$

Factor $- 1$ out of $- (91 x) - 1 (- 19)$ .

$\frac{- (91 x - 19)}{36} = - 2$

Rewrite $- (91 x - 19)$ as $- 1 (91 x - 19)$ .

$\frac{- 1 (91 x - 19)}{36} = - 2$

Move the negative in front of the fraction.

$- \frac{91 x - 19}{36} = - 2$

Multiply both sides of the equation by $- 36$ .

$- 36 (- \frac{91 x - 19}{36}) = - 36 \cdot - 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 36 (- \frac{91 x - 19}{36})$ .

Cancel the common factor of $36$ .

Move the leading negative in $- \frac{91 x - 19}{36}$ into the numerator.

$- 36 \frac{- (91 x - 19)}{36} = - 36 \cdot - 2$

Factor $36$ out of $- 36$ .

$36 (- 1) \frac{- (91 x - 19)}{36} = - 36 \cdot - 2$

Cancel the common factor.

$36 \cdot - 1 \frac{- (91 x - 19)}{36} = - 36 \cdot - 2$

Rewrite the expression.

$- - (91 x - 19) = - 36 \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (91 x - 19) = - 36 \cdot - 2$

Multiply $91 x - 19$ by $1$ .

$91 x - 19 = - 36 \cdot - 2$

Simplify the right side.

Multiply $- 36$ by $- 2$ .

$91 x - 19 = 72$

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

Add $19$ to both sides of the equation.

$91 x = 72 + 19$

Add $72$ and $19$ .

$91 x = 91$

Divide each term in $91 x = 91$ by $91$ and simplify.

Divide each term in $91 x = 91$ by $91$ .

$\frac{91 x}{91} = \frac{91}{91}$

Simplify the left side.

Cancel the common factor of $91$ .

Cancel the common factor.

$\frac{91 x}{91} = \frac{91}{91}$

Divide $x$ by $1$ .

$x = \frac{91}{91}$

Simplify the right side.

Divide $91$ by $91$ .

$x = 1$

Solve for x (x-1)/4+(2x+7)/9=3x-2

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