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

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

Simplify $\frac{x - 1}{3} + \frac{x + 5}{4}$ .

To write $\frac{x - 1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

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

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

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

Multiply $\frac{x - 1}{3}$ by $\frac{4}{4}$ .

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

Multiply $3$ by $4$ .

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

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

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

Multiply $4$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Move $4$ to the left of $x$ .

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

Multiply $- 1$ by $4$ .

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

Apply the distributive property.

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

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

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

Multiply $5$ by $3$ .

$\frac{4 x - 4 + 3 \cdot x + 15}{12} = \frac{1}{2}$

Add $4 x$ and $3 x$ .

$\frac{7 x - 4 + 15}{12} = \frac{1}{2}$

Add $- 4$ and $15$ .

$\frac{7 x + 11}{12} = \frac{1}{2}$

Multiply both sides by $12$ .

$\frac{7 x + 11}{12} \cdot 12 = \frac{1}{2} \cdot 12$

Simplify.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{7 x + 11}{12} \cdot 12 = \frac{1}{2} \cdot 12$

Rewrite the expression.

$7 x + 11 = \frac{1}{2} \cdot 12$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

$7 x + 11 = \frac{1}{2} \cdot (2 (6))$

Cancel the common factor.

$7 x + 11 = \frac{1}{2} \cdot (2 \cdot 6)$

Rewrite the expression.

$7 x + 11 = 6$

Solve for $x$ .

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

Subtract $11$ from both sides of the equation.

$7 x = 6 - 11$

Subtract $11$ from $6$ .

$7 x = - 5$

Divide each term in $7 x = - 5$ by $7$ and simplify.

Divide each term in $7 x = - 5$ by $7$ .

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.\overline{714285}$

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

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