Finite Math Examples

$- 8 (x + 6) - 5 (5 t + 1) = - 34 (t + 2) - 7$

Step 1

Simplify $- 8 (x + 6) - 5 (5 t + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 8 x - 8 \cdot 6 - 5 (5 t + 1) = - 34 (t + 2) - 7$

Step 1.1.2

Multiply $- 8$ by $6$ .

$- 8 x - 48 - 5 (5 t + 1) = - 34 (t + 2) - 7$

Step 1.1.3

Apply the distributive property.

$- 8 x - 48 - 5 (5 t) - 5 \cdot 1 = - 34 (t + 2) - 7$

Step 1.1.4

Multiply $5$ by $- 5$ .

$- 8 x - 48 - 25 t - 5 \cdot 1 = - 34 (t + 2) - 7$

Step 1.1.5

Multiply $- 5$ by $1$ .

$- 8 x - 48 - 25 t - 5 = - 34 (t + 2) - 7$

Step 1.2

Subtract $5$ from $- 48$ .

$- 8 x - 25 t - 53 = - 34 (t + 2) - 7$

Step 2

Simplify $- 34 (t + 2) - 7$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 8 x - 25 t - 53 = - 34 t - 34 \cdot 2 - 7$

Step 2.1.2

Multiply $- 34$ by $2$ .

$- 8 x - 25 t - 53 = - 34 t - 68 - 7$

Step 2.2

Subtract $7$ from $- 68$ .

$- 8 x - 25 t - 53 = - 34 t - 75$

Step 3

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

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Step 3.1

Add $34 t$ to both sides of the equation.

$- 8 x - 25 t - 53 + 34 t = - 75$

Step 3.2

Add $- 25 t$ and $34 t$ .

$- 8 x + 9 t - 53 = - 75$

Step 4

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

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Step 4.1

Add $8 x$ to both sides of the equation.

$9 t - 53 = - 75 + 8 x$

Step 4.2

Add $53$ to both sides of the equation.

$9 t = - 75 + 8 x + 53$

Step 4.3

Add $- 75$ and $53$ .

$9 t = 8 x - 22$

Step 5

Divide each term in $9 t = 8 x - 22$ by $9$ and simplify.

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Step 5.1

Divide each term in $9 t = 8 x - 22$ by $9$ .

$\frac{9 t}{9} = \frac{8 x}{9} + \frac{- 22}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 t}{9} = \frac{8 x}{9} + \frac{- 22}{9}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{8 x}{9} + \frac{- 22}{9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$t = \frac{8 x}{9} - \frac{22}{9}$