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

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

Step 1

Multiply both sides by $4$ .

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

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

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

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 1$ .

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

Add $1$ and $4$ .

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

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{5 - 2 x}{3}$ and $2$ .

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

Move $2$ to the left of $5 - 2 x$ .

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

Step 3

Solve for $x$ .

Multiply both sides by $3$ .

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

Simplify.

Simplify the left side.

Simplify $(x + 1) \cdot 3$ .

Apply the distributive property.

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

Simplify the expression.

Move $3$ to the left of $x$ .

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

Multiply $3$ by $1$ .

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

Simplify the right side.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$3 x + 3 = 2 (5 - 2 x)$

Apply the distributive property.

$3 x + 3 = 2 \cdot 5 + 2 (- 2 x)$

Simplify the expression.

Multiply $2$ by $5$ .

$3 x + 3 = 10 + 2 (- 2 x)$

Multiply $- 2$ by $2$ .

$3 x + 3 = 10 - 4 x$

Reorder $10$ and $- 4 x$ .

$3 x + 3 = - 4 x + 10$

Solve for $x$ .

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

Add $4 x$ to both sides of the equation.

$3 x + 3 + 4 x = 10$

Add $3 x$ and $4 x$ .

$7 x + 3 = 10$

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

Subtract $3$ from both sides of the equation.

$7 x = 10 - 3$

Subtract $3$ from $10$ .

$7 x = 7$

Divide each term in $7 x = 7$ by $7$ and simplify.

Divide each term in $7 x = 7$ by $7$ .

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $7$ by $7$ .

$x = 1$

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

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