Trigonometry Examples

$- \frac{5}{7} t = - 20$

Step 1

Multiply each term in $- \frac{5}{7} t = - 20$ by $- \frac{7}{5}$ .

$- \frac{5}{7} t (- \frac{7}{5}) = - 20 (- \frac{7}{5})$

Step 2

Simplify the left side.

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Step 2.1

Combine $t$ and $\frac{5}{7}$ .

$- \frac{t \cdot 5}{7} (- \frac{7}{5}) = - 20 (- \frac{7}{5})$

Step 2.2

Cancel the common factor of $5$ .

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Step 2.2.1

Move the leading negative in $- \frac{t \cdot 5}{7}$ into the numerator.

$\frac{- t \cdot 5}{7} (- \frac{7}{5}) = - 20 (- \frac{7}{5})$

Step 2.2.2

Move the leading negative in $- \frac{7}{5}$ into the numerator.

$\frac{- t \cdot 5}{7} \cdot \frac{- 7}{5} = - 20 (- \frac{7}{5})$

Step 2.2.3

Factor $5$ out of $- t \cdot 5$ .

$\frac{5 \cdot (- t)}{7} \cdot \frac{- 7}{5} = - 20 (- \frac{7}{5})$

Step 2.2.4

Cancel the common factor.

$\frac{5 \cdot (- t)}{7} \cdot \frac{- 7}{5} = - 20 (- \frac{7}{5})$

Step 2.2.5

Rewrite the expression.

$\frac{- t}{7} \cdot - 7 = - 20 (- \frac{7}{5})$

Step 2.3

Cancel the common factor of $7$ .

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Step 2.3.1

Factor $7$ out of $- 7$ .

$\frac{- t}{7} \cdot (7 (- 1)) = - 20 (- \frac{7}{5})$

Step 2.3.2

Cancel the common factor.

$\frac{- t}{7} \cdot (7 \cdot - 1) = - 20 (- \frac{7}{5})$

Step 2.3.3

Rewrite the expression.

$- t \cdot - 1 = - 20 (- \frac{7}{5})$

Step 2.4

Multiply.

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Step 2.4.1

Multiply $- 1$ by $- 1$ .

$1 t = - 20 (- \frac{7}{5})$

Step 2.4.2

Multiply $t$ by $1$ .

$t = - 20 (- \frac{7}{5})$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $5$ .

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Step 3.1.1

Move the leading negative in $- \frac{7}{5}$ into the numerator.

$t = - 20 (\frac{- 7}{5})$

Step 3.1.2

Factor $5$ out of $- 20$ .

$t = 5 (- 4) \frac{- 7}{5}$

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

$t = - 4 \cdot - 7$

Step 3.2

Multiply $- 4$ by $- 7$ .

$t = 28$