Finite Math Examples

$2 (t - 7) - 1 = - 5 (6 - t)$

Step 1

Simplify $2 (t - 7) - 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 t + 2 \cdot - 7 - 1 = - 5 (6 - t)$

Step 1.1.2

Multiply $2$ by $- 7$ .

$2 t - 14 - 1 = - 5 (6 - t)$

Step 1.2

Subtract $1$ from $- 14$ .

$2 t - 15 = - 5 (6 - t)$

Step 2

Simplify $- 5 (6 - t)$ .

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Step 2.1

Apply the distributive property.

$2 t - 15 = - 5 \cdot 6 - 5 (- t)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $- 5$ by $6$ .

$2 t - 15 = - 30 - 5 (- t)$

Step 2.2.2

Multiply $- 1$ by $- 5$ .

$2 t - 15 = - 30 + 5 t$

Step 3

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

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Step 3.1

Subtract $5 t$ from both sides of the equation.

$2 t - 15 - 5 t = - 30$

Step 3.2

Subtract $5 t$ from $2 t$ .

$- 3 t - 15 = - 30$

Step 4

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

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Step 4.1

Add $15$ to both sides of the equation.

$- 3 t = - 30 + 15$

Step 4.2

Add $- 30$ and $15$ .

$- 3 t = - 15$

Step 5

Divide each term in $- 3 t = - 15$ by $- 3$ and simplify.

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Step 5.1

Divide each term in $- 3 t = - 15$ by $- 3$ .

$\frac{- 3 t}{- 3} = \frac{- 15}{- 3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 3 t}{- 3} = \frac{- 15}{- 3}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 15}{- 3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 15$ by $- 3$ .

$t = 5$