Solve for u -4/3u-5/2=3/2u-6

$- \frac{4}{3} u - \frac{5}{2} = \frac{3}{2} u - 6$

Step 1

Simplify each term.

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

$- \frac{u \cdot 4}{3} - \frac{5}{2} = \frac{3}{2} u - 6$

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

$- \frac{4 u}{3} - \frac{5}{2} = \frac{3}{2} u - 6$

Step 2

Combine $\frac{3}{2}$ and $u$ .

$- \frac{4 u}{3} - \frac{5}{2} = \frac{3 u}{2} - 6$

Step 3

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

Subtract $\frac{3 u}{2}$ from both sides of the equation.

$- \frac{4 u}{3} - \frac{5}{2} - \frac{3 u}{2} = - 6$

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

$- \frac{4 u}{3} \cdot \frac{2}{2} - \frac{3 u}{2} - \frac{5}{2} = - 6$

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

$- \frac{4 u}{3} \cdot \frac{2}{2} - \frac{3 u}{2} \cdot \frac{3}{3} - \frac{5}{2} = - 6$

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

Multiply $\frac{4 u}{3}$ by $\frac{2}{2}$ .

$- \frac{4 u \cdot 2}{3 \cdot 2} - \frac{3 u}{2} \cdot \frac{3}{3} - \frac{5}{2} = - 6$

Multiply $3$ by $2$ .

$- \frac{4 u \cdot 2}{6} - \frac{3 u}{2} \cdot \frac{3}{3} - \frac{5}{2} = - 6$

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

$- \frac{4 u \cdot 2}{6} - \frac{3 u \cdot 3}{2 \cdot 3} - \frac{5}{2} = - 6$

Multiply $2$ by $3$ .

$- \frac{4 u \cdot 2}{6} - \frac{3 u \cdot 3}{6} - \frac{5}{2} = - 6$

Combine the numerators over the common denominator.

$\frac{- 4 u \cdot 2 - 3 u \cdot 3}{6} - \frac{5}{2} = - 6$

Simplify each term.

Simplify the numerator.

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

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

$\frac{u (- 4 \cdot 2) - 3 u \cdot 3}{6} - \frac{5}{2} = - 6$

Factor $u$ out of $- 3 u \cdot 3$ .

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

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

$\frac{u (- 4 \cdot 2 - 3 \cdot 3)}{6} - \frac{5}{2} = - 6$

Multiply $- 4$ by $2$ .

$\frac{u (- 8 - 3 \cdot 3)}{6} - \frac{5}{2} = - 6$

Multiply $- 3$ by $3$ .

$\frac{u (- 8 - 9)}{6} - \frac{5}{2} = - 6$

Subtract $9$ from $- 8$ .

$\frac{u \cdot - 17}{6} - \frac{5}{2} = - 6$

Move $- 17$ to the left of $u$ .

$\frac{- 17 \cdot u}{6} - \frac{5}{2} = - 6$

Move the negative in front of the fraction.

$- \frac{17 u}{6} - \frac{5}{2} = - 6$

Step 4

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

Add $\frac{5}{2}$ to both sides of the equation.

$- \frac{17 u}{6} = - 6 + \frac{5}{2}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{17 u}{6} = - 6 \cdot \frac{2}{2} + \frac{5}{2}$

Combine $- 6$ and $\frac{2}{2}$ .

$- \frac{17 u}{6} = \frac{- 6 \cdot 2}{2} + \frac{5}{2}$

Combine the numerators over the common denominator.

$- \frac{17 u}{6} = \frac{- 6 \cdot 2 + 5}{2}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$- \frac{17 u}{6} = \frac{- 12 + 5}{2}$

Add $- 12$ and $5$ .

$- \frac{17 u}{6} = \frac{- 7}{2}$

Move the negative in front of the fraction.

$- \frac{17 u}{6} = - \frac{7}{2}$

Step 5

Multiply both sides of the equation by $- \frac{6}{17}$ .

$- \frac{6}{17} (- \frac{17 u}{6}) = - \frac{6}{17} (- \frac{7}{2})$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{17} (- \frac{17 u}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{17}$ into the numerator.

$\frac{- 6}{17} (- \frac{17 u}{6}) = - \frac{6}{17} (- \frac{7}{2})$

Move the leading negative in $- \frac{17 u}{6}$ into the numerator.

$\frac{- 6}{17} \cdot \frac{- 17 u}{6} = - \frac{6}{17} (- \frac{7}{2})$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{17} \cdot \frac{- 17 u}{6} = - \frac{6}{17} (- \frac{7}{2})$

Cancel the common factor.

$\frac{6 \cdot - 1}{17} \cdot \frac{- 17 u}{6} = - \frac{6}{17} (- \frac{7}{2})$

Rewrite the expression.

$\frac{- 1}{17} (- 17 u) = - \frac{6}{17} (- \frac{7}{2})$

Cancel the common factor of $17$ .

Factor $17$ out of $- 17 u$ .

$\frac{- 1}{17} (17 (- u)) = - \frac{6}{17} (- \frac{7}{2})$

Cancel the common factor.

$\frac{- 1}{17} (17 (- u)) = - \frac{6}{17} (- \frac{7}{2})$

Rewrite the expression.

$- - u = - \frac{6}{17} (- \frac{7}{2})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 u = - \frac{6}{17} (- \frac{7}{2})$

Multiply $u$ by $1$ .

$u = - \frac{6}{17} (- \frac{7}{2})$

Simplify the right side.

Simplify $- \frac{6}{17} (- \frac{7}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{6}{17}$ into the numerator.

$u = \frac{- 6}{17} (- \frac{7}{2})$

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$u = \frac{- 6}{17} \cdot \frac{- 7}{2}$

Factor $2$ out of $- 6$ .

$u = \frac{2 (- 3)}{17} \cdot \frac{- 7}{2}$

Cancel the common factor.

$u = \frac{2 \cdot - 3}{17} \cdot \frac{- 7}{2}$

Rewrite the expression.

$u = \frac{- 3}{17} \cdot - 7$

Combine $\frac{- 3}{17}$ and $- 7$ .

$u = \frac{- 3 \cdot - 7}{17}$

Multiply $- 3$ by $- 7$ .

$u = \frac{21}{17}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$u = \frac{21}{17}$

Decimal Form:

$u = 1.23529411 \dots$

Mixed Number Form:

$u = 1 \frac{4}{17}$

Solve for u -4/3u-5/2=3/2u-6

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