Solve for x (3x-2)/4-(2x+5)/3=(1-x)/6

$\frac{3 x - 2}{4} - \frac{2 x + 5}{3} = \frac{1 - x}{6}$

Step 1

Multiply both sides by $6$ .

$(\frac{3 x - 2}{4} - \frac{2 x + 5}{3}) \cdot 6 = \frac{1 - x}{6} \cdot 6$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{3 x - 2}{4} - \frac{2 x + 5}{3}) \cdot 6$ .

To write $\frac{3 x - 2}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{3 x - 2}{4} \cdot \frac{3}{3} - \frac{2 x + 5}{3}) \cdot 6 = \frac{1 - x}{6} \cdot 6$

To write $- \frac{2 x + 5}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{3 x - 2}{4} \cdot \frac{3}{3} - \frac{2 x + 5}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{1 - x}{6} \cdot 6$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x - 2}{4}$ by $\frac{3}{3}$ .

$(\frac{(3 x - 2) \cdot 3}{4 \cdot 3} - \frac{2 x + 5}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $4$ by $3$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{2 x + 5}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $\frac{2 x + 5}{3}$ by $\frac{4}{4}$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{(2 x + 5) \cdot 4}{3 \cdot 4}) \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $3$ by $4$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{(2 x + 5) \cdot 4}{12}) \cdot 6 = \frac{1 - x}{6} \cdot 6$

Combine the numerators over the common denominator.

$\frac{(3 x - 2) \cdot 3 - (2 x + 5) \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x \cdot 3 - 2 \cdot 3 - (2 x + 5) \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $3$ by $3$ .

$\frac{9 x - 2 \cdot 3 - (2 x + 5) \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $- 2$ by $3$ .

$\frac{9 x - 6 - (2 x + 5) \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Apply the distributive property.

$\frac{9 x - 6 + (- (2 x) - 1 \cdot 5) \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $2$ by $- 1$ .

$\frac{9 x - 6 + (- 2 x - 1 \cdot 5) \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $- 1$ by $5$ .

$\frac{9 x - 6 + (- 2 x - 5) \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Apply the distributive property.

$\frac{9 x - 6 - 2 x \cdot 4 - 5 \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $4$ by $- 2$ .

$\frac{9 x - 6 - 8 x - 5 \cdot 4}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Multiply $- 5$ by $4$ .

$\frac{9 x - 6 - 8 x - 20}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Subtract $8 x$ from $9 x$ .

$\frac{x - 6 - 20}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Subtract $20$ from $- 6$ .

$\frac{x - 26}{12} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$\frac{x - 26}{6 (2)} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Cancel the common factor.

$\frac{x - 26}{6 \cdot 2} \cdot 6 = \frac{1 - x}{6} \cdot 6$

Rewrite the expression.

$\frac{x - 26}{2} = \frac{1 - x}{6} \cdot 6$

Simplify the right side.

Simplify $\frac{1 - x}{6} \cdot 6$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{x - 26}{2} = \frac{1 - x}{6} \cdot 6$

Rewrite the expression.

$\frac{x - 26}{2} = 1 - x$

Reorder $1$ and $- x$ .

$\frac{x - 26}{2} = - x + 1$

Step 3

Solve for $x$ .

Multiply both sides by $2$ .

$\frac{x - 26}{2} \cdot 2 = (- x + 1) \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x - 26}{2} \cdot 2 = (- x + 1) \cdot 2$

Rewrite the expression.

$x - 26 = (- x + 1) \cdot 2$

Simplify the right side.

Simplify $(- x + 1) \cdot 2$ .

Apply the distributive property.

$x - 26 = - x \cdot 2 + 1 \cdot 2$

Multiply.

Multiply $2$ by $- 1$ .

$x - 26 = - 2 x + 1 \cdot 2$

Multiply $2$ by $1$ .

$x - 26 = - 2 x + 2$

Solve for $x$ .

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

Add $2 x$ to both sides of the equation.

$x - 26 + 2 x = 2$

Add $x$ and $2 x$ .

$3 x - 26 = 2$

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

Add $26$ to both sides of the equation.

$3 x = 2 + 26$

Add $2$ and $26$ .

$3 x = 28$

Divide each term in $3 x = 28$ by $3$ and simplify.

Divide each term in $3 x = 28$ by $3$ .

$\frac{3 x}{3} = \frac{28}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{28}{3}$

Divide $x$ by $1$ .

$x = \frac{28}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{28}{3}$

Decimal Form:

$x = 9.\overline{3}$

Mixed Number Form:

$x = 9 \frac{1}{3}$

Solve for x (3x-2)/4-(2x+5)/3=(1-x)/6

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