Solve for u 2u-2/3=-3/4u+3

$2 u - \frac{2}{3} = - \frac{3}{4} u + 3$

Step 1

Simplify each term.

Combine $u$ and $\frac{3}{4}$ .

$2 u - \frac{2}{3} = - \frac{u \cdot 3}{4} + 3$

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

$2 u - \frac{2}{3} = - \frac{3 u}{4} + 3$

Step 2

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

Add $\frac{3 u}{4}$ to both sides of the equation.

$2 u - \frac{2}{3} + \frac{3 u}{4} = 3$

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

$2 u \cdot \frac{4}{4} + \frac{3 u}{4} - \frac{2}{3} = 3$

Combine $2 u$ and $\frac{4}{4}$ .

$\frac{2 u \cdot 4}{4} + \frac{3 u}{4} - \frac{2}{3} = 3$

Combine the numerators over the common denominator.

$\frac{2 u \cdot 4 + 3 u}{4} - \frac{2}{3} = 3$

Simplify each term.

Simplify the numerator.

Factor $u$ out of $2 u \cdot 4 + 3 u$ .

Factor $u$ out of $2 u \cdot 4$ .

$\frac{u (2 \cdot 4) + 3 u}{4} - \frac{2}{3} = 3$

Factor $u$ out of $3 u$ .

$\frac{u (2 \cdot 4) + u \cdot 3}{4} - \frac{2}{3} = 3$

Factor $u$ out of $u (2 \cdot 4) + u \cdot 3$ .

$\frac{u (2 \cdot 4 + 3)}{4} - \frac{2}{3} = 3$

Multiply $2$ by $4$ .

$\frac{u (8 + 3)}{4} - \frac{2}{3} = 3$

Add $8$ and $3$ .

$\frac{u \cdot 11}{4} - \frac{2}{3} = 3$

Move $11$ to the left of $u$ .

$\frac{11 u}{4} - \frac{2}{3} = 3$

Step 3

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

Add $\frac{2}{3}$ to both sides of the equation.

$\frac{11 u}{4} = 3 + \frac{2}{3}$

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

$\frac{11 u}{4} = 3 \cdot \frac{3}{3} + \frac{2}{3}$

Combine $3$ and $\frac{3}{3}$ .

$\frac{11 u}{4} = \frac{3 \cdot 3}{3} + \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{11 u}{4} = \frac{3 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{11 u}{4} = \frac{9 + 2}{3}$

Add $9$ and $2$ .

$\frac{11 u}{4} = \frac{11}{3}$

Step 4

Multiply both sides of the equation by $\frac{4}{11}$ .

$\frac{4}{11} \cdot \frac{11 u}{4} = \frac{4}{11} \cdot \frac{11}{3}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{11} \cdot \frac{11 u}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{11} \cdot \frac{11 u}{4} = \frac{4}{11} \cdot \frac{11}{3}$

Rewrite the expression.

$\frac{1}{11} (11 u) = \frac{4}{11} \cdot \frac{11}{3}$

Cancel the common factor of $11$ .

Factor $11$ out of $11 u$ .

$\frac{1}{11} (11 (u)) = \frac{4}{11} \cdot \frac{11}{3}$

Cancel the common factor.

$\frac{1}{11} (11 u) = \frac{4}{11} \cdot \frac{11}{3}$

Rewrite the expression.

$u = \frac{4}{11} \cdot \frac{11}{3}$

Simplify the right side.

Simplify $\frac{4}{11} \cdot \frac{11}{3}$ .

Cancel the common factor of $11$ .

Cancel the common factor.

$u = \frac{4}{11} \cdot \frac{11}{3}$

Rewrite the expression.

$u = 4 (\frac{1}{3})$

Combine $4$ and $\frac{1}{3}$ .

$u = \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$u = \frac{4}{3}$

Decimal Form:

$u = 1.\overline{3}$

Mixed Number Form:

$u = 1 \frac{1}{3}$

Solve for u 2u-2/3=-3/4u+3

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