Algebra Examples

$4 (9 + 3 t) - 12 = - 6$

Step 1

Simplify $4 (9 + 3 t) - 12$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 \cdot 9 + 4 (3 t) - 12 = - 6$

Step 1.1.2

Multiply $4$ by $9$ .

$36 + 4 (3 t) - 12 = - 6$

Step 1.1.3

Multiply $3$ by $4$ .

$36 + 12 t - 12 = - 6$

$36 + 12 t - 12 = - 6$

Step 1.2

Subtract $12$ from $36$ .

$12 t + 24 = - 6$

$12 t + 24 = - 6$

Step 2

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

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Step 2.1

Subtract $24$ from both sides of the equation.

$12 t = - 6 - 24$

Step 2.2

Subtract $24$ from $- 6$ .

$12 t = - 30$

$12 t = - 30$

Step 3

Divide each term in $12 t = - 30$ by $12$ and simplify.

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Step 3.1

Divide each term in $12 t = - 30$ by $12$ .

$\frac{12 t}{12} = \frac{- 30}{12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12 t}{12} = \frac{- 30}{12}$

Step 3.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 30}{12}$

$t = \frac{- 30}{12}$

$t = \frac{- 30}{12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $- 30$ and $12$ .

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Step 3.3.1.1

Factor $6$ out of $- 30$ .

$t = \frac{6 (- 5)}{12}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $6$ out of $12$ .

$t = \frac{6 \cdot - 5}{6 \cdot 2}$

Step 3.3.1.2.2

Cancel the common factor.

$t = \frac{6 \cdot - 5}{6 \cdot 2}$

Step 3.3.1.2.3

Rewrite the expression.

$t = \frac{- 5}{2}$

$t = \frac{- 5}{2}$

$t = \frac{- 5}{2}$

Step 3.3.2

Move the negative in front of the fraction.

$t = - \frac{5}{2}$

$t = - \frac{5}{2}$

$t = - \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{5}{2}$

Decimal Form:

$t = - 2.5$

Mixed Number Form:

$t = - 2 \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$