Solve for t 16-2t=3/2t+9

$16 - 2 t = \frac{3}{2} t + 9$

Step 1

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

$16 - 2 t = \frac{3 t}{2} + 9$

Step 2

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

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

$16 - 2 t - \frac{3 t}{2} = 9$

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

$16 - 2 t \cdot \frac{2}{2} - \frac{3 t}{2} = 9$

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

$16 + \frac{- 2 t \cdot 2}{2} - \frac{3 t}{2} = 9$

Combine the numerators over the common denominator.

$16 + \frac{- 2 t \cdot 2 - 3 t}{2} = 9$

Simplify each term.

Simplify the numerator.

Factor $t$ out of $- 2 t \cdot 2 - 3 t$ .

Factor $t$ out of $- 2 t \cdot 2$ .

$16 + \frac{t (- 2 \cdot 2) - 3 t}{2} = 9$

Factor $t$ out of $- 3 t$ .

$16 + \frac{t (- 2 \cdot 2) + t \cdot - 3}{2} = 9$

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

$16 + \frac{t (- 2 \cdot 2 - 3)}{2} = 9$

Multiply $- 2$ by $2$ .

$16 + \frac{t (- 4 - 3)}{2} = 9$

Subtract $3$ from $- 4$ .

$16 + \frac{t \cdot - 7}{2} = 9$

Move $- 7$ to the left of $t$ .

$16 + \frac{- 7 \cdot t}{2} = 9$

Move the negative in front of the fraction.

$16 - \frac{7 t}{2} = 9$

Step 3

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

Subtract $16$ from both sides of the equation.

$- \frac{7 t}{2} = 9 - 16$

Subtract $16$ from $9$ .

$- \frac{7 t}{2} = - 7$

Step 4

Multiply both sides of the equation by $- \frac{2}{7}$ .

$- \frac{2}{7} (- \frac{7 t}{2}) = - \frac{2}{7} \cdot - 7$

Step 5

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

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

$\frac{- 2}{7} (- \frac{7 t}{2}) = - \frac{2}{7} \cdot - 7$

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

$\frac{- 2}{7} \cdot \frac{- 7 t}{2} = - \frac{2}{7} \cdot - 7$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{7} \cdot \frac{- 7 t}{2} = - \frac{2}{7} \cdot - 7$

Cancel the common factor.

$\frac{2 \cdot - 1}{7} \cdot \frac{- 7 t}{2} = - \frac{2}{7} \cdot - 7$

Rewrite the expression.

$\frac{- 1}{7} (- 7 t) = - \frac{2}{7} \cdot - 7$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 t$ .

$\frac{- 1}{7} (7 (- t)) = - \frac{2}{7} \cdot - 7$

Cancel the common factor.

$\frac{- 1}{7} (7 (- t)) = - \frac{2}{7} \cdot - 7$

Rewrite the expression.

$- - t = - \frac{2}{7} \cdot - 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 t = - \frac{2}{7} \cdot - 7$

Multiply $t$ by $1$ .

$t = - \frac{2}{7} \cdot - 7$

Simplify the right side.

Simplify $- \frac{2}{7} \cdot - 7$ .

Cancel the common factor of $7$ .

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

$t = \frac{- 2}{7} \cdot - 7$

Factor $7$ out of $- 7$ .

$t = \frac{- 2}{7} \cdot (7 (- 1))$

Cancel the common factor.

$t = \frac{- 2}{7} \cdot (7 \cdot - 1)$

Rewrite the expression.

$t = - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$t = 2$

Solve for t 16-2t=3/2t+9

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