Solve for t 4t+14=(6t)/5+7

$4 t + 14 = \frac{6 t}{5} + 7$

Step 1

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

Subtract $\frac{6 t}{5}$ from both sides of the equation.

$4 t + 14 - \frac{6 t}{5} = 7$

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

$4 t \cdot \frac{5}{5} - \frac{6 t}{5} + 14 = 7$

Combine $4 t$ and $\frac{5}{5}$ .

$\frac{4 t \cdot 5}{5} - \frac{6 t}{5} + 14 = 7$

Combine the numerators over the common denominator.

$\frac{4 t \cdot 5 - 6 t}{5} + 14 = 7$

Simplify the numerator.

Factor $2 t$ out of $4 t \cdot 5 - 6 t$ .

Factor $2 t$ out of $4 t \cdot 5$ .

$\frac{2 t (2 \cdot 5) - 6 t}{5} + 14 = 7$

Factor $2 t$ out of $- 6 t$ .

$\frac{2 t (2 \cdot 5) + 2 t (- 3)}{5} + 14 = 7$

Factor $2 t$ out of $2 t (2 \cdot 5) + 2 t (- 3)$ .

$\frac{2 t (2 \cdot 5 - 3)}{5} + 14 = 7$

Multiply $2$ by $5$ .

$\frac{2 t (10 - 3)}{5} + 14 = 7$

Subtract $3$ from $10$ .

$\frac{2 t \cdot 7}{5} + 14 = 7$

Multiply $7$ by $2$ .

$\frac{14 t}{5} + 14 = 7$

Step 2

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

Subtract $14$ from both sides of the equation.

$\frac{14 t}{5} = 7 - 14$

Subtract $14$ from $7$ .

$\frac{14 t}{5} = - 7$

Step 3

Multiply both sides of the equation by $\frac{5}{14}$ .

$\frac{5}{14} \cdot \frac{14 t}{5} = \frac{5}{14} \cdot - 7$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{14} \cdot \frac{14 t}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{14} \cdot \frac{14 t}{5} = \frac{5}{14} \cdot - 7$

Rewrite the expression.

$\frac{1}{14} (14 t) = \frac{5}{14} \cdot - 7$

Cancel the common factor of $14$ .

Factor $14$ out of $14 t$ .

$\frac{1}{14} (14 (t)) = \frac{5}{14} \cdot - 7$

Cancel the common factor.

$\frac{1}{14} (14 t) = \frac{5}{14} \cdot - 7$

Rewrite the expression.

$t = \frac{5}{14} \cdot - 7$

Simplify the right side.

Simplify $\frac{5}{14} \cdot - 7$ .

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

$t = \frac{5}{7 (2)} \cdot - 7$

Factor $7$ out of $- 7$ .

$t = \frac{5}{7 \cdot 2} \cdot (7 \cdot - 1)$

Cancel the common factor.

$t = \frac{5}{7 \cdot 2} \cdot (7 \cdot - 1)$

Rewrite the expression.

$t = \frac{5}{2} \cdot - 1$

Combine $\frac{5}{2}$ and $- 1$ .

$t = \frac{5 \cdot - 1}{2}$

Simplify the expression.

Multiply $5$ by $- 1$ .

$t = \frac{- 5}{2}$

Move the negative in front of the fraction.

$t = - \frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{5}{2}$

Decimal Form:

$t = - 2.5$

Mixed Number Form:

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

Solve for t 4t+14=(6t)/5+7

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