Solve for x (3x+1)/3-13/2=(1-x)/4

$\frac{3 x + 1}{3} - \frac{13}{2} = \frac{1 - x}{4}$

Step 1

Multiply both sides by $4$ .

$(\frac{3 x + 1}{3} - \frac{13}{2}) \cdot 4 = \frac{1 - x}{4} \cdot 4$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{3 x + 1}{3} - \frac{13}{2}) \cdot 4$ .

To write $\frac{3 x + 1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{3 x + 1}{3} \cdot \frac{2}{2} - \frac{13}{2}) \cdot 4 = \frac{1 - x}{4} \cdot 4$

To write $- \frac{13}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{3 x + 1}{3} \cdot \frac{2}{2} - \frac{13}{2} \cdot \frac{3}{3}) \cdot 4 = \frac{1 - x}{4} \cdot 4$

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

Multiply $\frac{3 x + 1}{3}$ by $\frac{2}{2}$ .

$(\frac{(3 x + 1) \cdot 2}{3 \cdot 2} - \frac{13}{2} \cdot \frac{3}{3}) \cdot 4 = \frac{1 - x}{4} \cdot 4$

Multiply $3$ by $2$ .

$(\frac{(3 x + 1) \cdot 2}{6} - \frac{13}{2} \cdot \frac{3}{3}) \cdot 4 = \frac{1 - x}{4} \cdot 4$

Multiply $\frac{13}{2}$ by $\frac{3}{3}$ .

$(\frac{(3 x + 1) \cdot 2}{6} - \frac{13 \cdot 3}{2 \cdot 3}) \cdot 4 = \frac{1 - x}{4} \cdot 4$

Multiply $2$ by $3$ .

$(\frac{(3 x + 1) \cdot 2}{6} - \frac{13 \cdot 3}{6}) \cdot 4 = \frac{1 - x}{4} \cdot 4$

Combine the numerators over the common denominator.

$\frac{(3 x + 1) \cdot 2 - 13 \cdot 3}{6} \cdot 4 = \frac{1 - x}{4} \cdot 4$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x \cdot 2 + 1 \cdot 2 - 13 \cdot 3}{6} \cdot 4 = \frac{1 - x}{4} \cdot 4$

Multiply $2$ by $3$ .

$\frac{6 x + 1 \cdot 2 - 13 \cdot 3}{6} \cdot 4 = \frac{1 - x}{4} \cdot 4$

Multiply $2$ by $1$ .

$\frac{6 x + 2 - 13 \cdot 3}{6} \cdot 4 = \frac{1 - x}{4} \cdot 4$

Multiply $- 13$ by $3$ .

$\frac{6 x + 2 - 39}{6} \cdot 4 = \frac{1 - x}{4} \cdot 4$

Subtract $39$ from $2$ .

$\frac{6 x - 37}{6} \cdot 4 = \frac{1 - x}{4} \cdot 4$

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{6 x - 37}{2 (3)} \cdot 4 = \frac{1 - x}{4} \cdot 4$

Factor $2$ out of $4$ .

$\frac{6 x - 37}{2 \cdot 3} \cdot (2 \cdot 2) = \frac{1 - x}{4} \cdot 4$

Cancel the common factor.

$\frac{6 x - 37}{2 \cdot 3} \cdot (2 \cdot 2) = \frac{1 - x}{4} \cdot 4$

Rewrite the expression.

$\frac{6 x - 37}{3} \cdot 2 = \frac{1 - x}{4} \cdot 4$

Combine $\frac{6 x - 37}{3}$ and $2$ .

$\frac{(6 x - 37) \cdot 2}{3} = \frac{1 - x}{4} \cdot 4$

Move $2$ to the left of $6 x - 37$ .

$\frac{2 (6 x - 37)}{3} = \frac{1 - x}{4} \cdot 4$

Simplify the right side.

Simplify $\frac{1 - x}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{2 (6 x - 37)}{3} = \frac{1 - x}{4} \cdot 4$

Rewrite the expression.

$\frac{2 (6 x - 37)}{3} = 1 - x$

Reorder $1$ and $- x$ .

$\frac{2 (6 x - 37)}{3} = - x + 1$

Step 3

Solve for $x$ .

Multiply both sides by $3$ .

$\frac{2 (6 x - 37)}{3} \cdot 3 = (- x + 1) \cdot 3$

Simplify.

Simplify the left side.

Simplify $\frac{2 (6 x - 37)}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 (6 x - 37)}{3} \cdot 3 = (- x + 1) \cdot 3$

Rewrite the expression.

$2 (6 x - 37) = (- x + 1) \cdot 3$

Apply the distributive property.

$2 (6 x) + 2 \cdot - 37 = (- x + 1) \cdot 3$

Multiply.

Multiply $6$ by $2$ .

$12 x + 2 \cdot - 37 = (- x + 1) \cdot 3$

Multiply $2$ by $- 37$ .

$12 x - 74 = (- x + 1) \cdot 3$

Simplify the right side.

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

Apply the distributive property.

$12 x - 74 = - x \cdot 3 + 1 \cdot 3$

Multiply.

Multiply $3$ by $- 1$ .

$12 x - 74 = - 3 x + 1 \cdot 3$

Multiply $3$ by $1$ .

$12 x - 74 = - 3 x + 3$

Solve for $x$ .

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

Add $3 x$ to both sides of the equation.

$12 x - 74 + 3 x = 3$

Add $12 x$ and $3 x$ .

$15 x - 74 = 3$

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

Add $74$ to both sides of the equation.

$15 x = 3 + 74$

Add $3$ and $74$ .

$15 x = 77$

Divide each term in $15 x = 77$ by $15$ and simplify.

Divide each term in $15 x = 77$ by $15$ .

$\frac{15 x}{15} = \frac{77}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 x}{15} = \frac{77}{15}$

Divide $x$ by $1$ .

$x = \frac{77}{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{77}{15}$

Decimal Form:

$x = 5.1\overline{3}$

Mixed Number Form:

$x = 5 \frac{2}{15}$

Solve for x (3x+1)/3-13/2=(1-x)/4

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