Pre-Algebra Examples

$(7 t - 2) - (- 3 t + 1) = - 3 (1 - 3 t)$

Step 1

Simplify $7 t - 2 - (- 3 t + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$7 t - 2 - (- 3 t) - 1 \cdot 1 = - 3 (1 - 3 t)$

Step 1.1.2

Multiply $- 3$ by $- 1$ .

$7 t - 2 + 3 t - 1 \cdot 1 = - 3 (1 - 3 t)$

Step 1.1.3

Multiply $- 1$ by $1$ .

$7 t - 2 + 3 t - 1 = - 3 (1 - 3 t)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $7 t$ and $3 t$ .

$10 t - 2 - 1 = - 3 (1 - 3 t)$

Step 1.2.2

Subtract $1$ from $- 2$ .

$10 t - 3 = - 3 (1 - 3 t)$

Step 2

Simplify $- 3 (1 - 3 t)$ .

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Step 2.1

Apply the distributive property.

$10 t - 3 = - 3 \cdot 1 - 3 (- 3 t)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $- 3$ by $1$ .

$10 t - 3 = - 3 - 3 (- 3 t)$

Step 2.2.2

Multiply $- 3$ by $- 3$ .

$10 t - 3 = - 3 + 9 t$

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.

$10 t - 3 - 9 t = - 3$

Step 3.2

Subtract $9 t$ from $10 t$ .

$t - 3 = - 3$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$t = - 3 + 3$

Step 4.2

Add $- 3$ and $3$ .

$t = 0$