Basic Math Examples

$3 (5 - 3 (4 - t)) - 2 = 8 - 3 (5 t - 4)$

Step 1

Simplify $3 (5 - 3 (4 - t)) - 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$3 (5 - 3 \cdot 4 - 3 (- t)) - 2 = 8 - 3 (5 t - 4)$

Step 1.1.1.2

Multiply $- 3$ by $4$ .

$3 (5 - 12 - 3 (- t)) - 2 = 8 - 3 (5 t - 4)$

Step 1.1.1.3

Multiply $- 1$ by $- 3$ .

$3 (5 - 12 + 3 t) - 2 = 8 - 3 (5 t - 4)$

Step 1.1.2

Subtract $12$ from $5$ .

$3 (- 7 + 3 t) - 2 = 8 - 3 (5 t - 4)$

Step 1.1.3

Apply the distributive property.

$3 \cdot - 7 + 3 (3 t) - 2 = 8 - 3 (5 t - 4)$

Step 1.1.4

Multiply $3$ by $- 7$ .

$- 21 + 3 (3 t) - 2 = 8 - 3 (5 t - 4)$

Step 1.1.5

Multiply $3$ by $3$ .

$- 21 + 9 t - 2 = 8 - 3 (5 t - 4)$

Step 1.2

Subtract $2$ from $- 21$ .

$9 t - 23 = 8 - 3 (5 t - 4)$

Step 2

Simplify $8 - 3 (5 t - 4)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$9 t - 23 = 8 - 3 (5 t) - 3 \cdot - 4$

Step 2.1.2

Multiply $5$ by $- 3$ .

$9 t - 23 = 8 - 15 t - 3 \cdot - 4$

Step 2.1.3

Multiply $- 3$ by $- 4$ .

$9 t - 23 = 8 - 15 t + 12$

Step 2.2

Add $8$ and $12$ .

$9 t - 23 = - 15 t + 20$

Step 3

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

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Step 3.1

Add $15 t$ to both sides of the equation.

$9 t - 23 + 15 t = 20$

Step 3.2

Add $9 t$ and $15 t$ .

$24 t - 23 = 20$

Step 4

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

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Step 4.1

Add $23$ to both sides of the equation.

$24 t = 20 + 23$

Step 4.2

Add $20$ and $23$ .

$24 t = 43$

Step 5

Divide each term in $24 t = 43$ by $24$ and simplify.

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Step 5.1

Divide each term in $24 t = 43$ by $24$ .

$\frac{24 t}{24} = \frac{43}{24}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $24$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{24 t}{24} = \frac{43}{24}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{43}{24}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \frac{43}{24}$

Decimal Form:

$t = 1.791\overline{6}$

Mixed Number Form:

$t = 1 \frac{19}{24}$