Pre-Algebra Examples

$6 (t - 1) = 9 (t - 4)$

Step 1

Simplify $6 (t - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + 6 (t - 1) = 9 (t - 4)$

Step 1.2

Simplify by adding zeros.

$6 (t - 1) = 9 (t - 4)$

Step 1.3

Apply the distributive property.

$6 t + 6 \cdot - 1 = 9 (t - 4)$

Step 1.4

Multiply $6$ by $- 1$ .

$6 t - 6 = 9 (t - 4)$

Step 2

Simplify $9 (t - 4)$ .

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Step 2.1

Apply the distributive property.

$6 t - 6 = 9 t + 9 \cdot - 4$

Step 2.2

Multiply $9$ by $- 4$ .

$6 t - 6 = 9 t - 36$

Step 3

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

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Step 3.1

Subtract $9 t$ from both sides of the equation.

$6 t - 6 - 9 t = - 36$

Step 3.2

Subtract $9 t$ from $6 t$ .

$- 3 t - 6 = - 36$

Step 4

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

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Step 4.1

Add $6$ to both sides of the equation.

$- 3 t = - 36 + 6$

Step 4.2

Add $- 36$ and $6$ .

$- 3 t = - 30$

Step 5

Divide each term in $- 3 t = - 30$ by $- 3$ and simplify.

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Step 5.1

Divide each term in $- 3 t = - 30$ by $- 3$ .

$\frac{- 3 t}{- 3} = \frac{- 30}{- 3}$

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.

$\frac{- 3 t}{- 3} = \frac{- 30}{- 3}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 30}{- 3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 30$ by $- 3$ .

$t = 10$