Basic Math Examples

$4 t + 17 - 4 w = w (2 t)$

Step 1

Rewrite using the commutative property of multiplication.

$4 t + 17 - 4 w = 2 w t$

Step 2

Subtract $2 w t$ from both sides of the equation.

$4 t + 17 - 4 w - 2 w t = 0$

Step 3

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

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Step 3.1

Subtract $17$ from both sides of the equation.

$4 t - 4 w - 2 w t = - 17$

Step 3.2

Add $4 w$ to both sides of the equation.

$4 t - 2 w t = - 17 + 4 w$

Step 4

Factor $2 t$ out of $4 t - 2 w t$ .

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Step 4.1

Factor $2 t$ out of $4 t$ .

$2 t (2) - 2 w t = - 17 + 4 w$

Step 4.2

Factor $2 t$ out of $- 2 w t$ .

$2 t (2) + 2 t (- w) = - 17 + 4 w$

Step 4.3

Factor $2 t$ out of $2 t (2) + 2 t (- w)$ .

$2 t (2 - w) = - 17 + 4 w$

Step 5

Divide each term in $2 t (2 - w) = - 17 + 4 w$ by $2 (2 - w)$ and simplify.

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Step 5.1

Divide each term in $2 t (2 - w) = - 17 + 4 w$ by $2 (2 - w)$ .

$\frac{2 t (2 - w)}{2 (2 - w)} = \frac{- 17}{2 (2 - w)} + \frac{4 w}{2 (2 - w)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 t (2 - w)}{2 (2 - w)} = \frac{- 17}{2 (2 - w)} + \frac{4 w}{2 (2 - w)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{t (2 - w)}{2 - w} = \frac{- 17}{2 (2 - w)} + \frac{4 w}{2 (2 - w)}$

Step 5.2.2

Cancel the common factor of $2 - w$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{t (2 - w)}{2 - w} = \frac{- 17}{2 (2 - w)} + \frac{4 w}{2 (2 - w)}$

Step 5.2.2.2

Divide $t$ by $1$ .

$t = \frac{- 17}{2 (2 - w)} + \frac{4 w}{2 (2 - w)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Move the negative in front of the fraction.

$t = - \frac{17}{2 (2 - w)} + \frac{4 w}{2 (2 - w)}$

Step 5.3.1.2

Cancel the common factor of $4$ and $2$ .

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Step 5.3.1.2.1

Factor $2$ out of $4 w$ .

$t = - \frac{17}{2 (2 - w)} + \frac{2 (2 w)}{2 (2 - w)}$

Step 5.3.1.2.2

Cancel the common factors.

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Step 5.3.1.2.2.1

Cancel the common factor.

$t = - \frac{17}{2 (2 - w)} + \frac{2 (2 w)}{2 (2 - w)}$

Step 5.3.1.2.2.2

Rewrite the expression.

$t = - \frac{17}{2 (2 - w)} + \frac{2 w}{2 - w}$

Step 5.3.2

To write $\frac{2 w}{2 - w}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$t = - \frac{17}{2 (2 - w)} + \frac{2 w}{2 - w} \cdot \frac{2}{2}$

Step 5.3.3

Write each expression with a common denominator of $2 (2 - w)$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.3.3.1

Multiply $\frac{2 w}{2 - w}$ by $\frac{2}{2}$ .

$t = - \frac{17}{2 (2 - w)} + \frac{2 w \cdot 2}{(2 - w) \cdot 2}$

Step 5.3.3.2

Reorder the factors of $(2 - w) \cdot 2$ .

$t = - \frac{17}{2 (2 - w)} + \frac{2 w \cdot 2}{2 (2 - w)}$

Step 5.3.4

Combine the numerators over the common denominator.

$t = \frac{- 17 + 2 w \cdot 2}{2 (2 - w)}$

Step 5.3.5

Multiply $2$ by $2$ .

$t = \frac{- 17 + 4 w}{2 (2 - w)}$

Step 5.3.6

Rewrite $- 17$ as $- 1 (17)$ .

$t = \frac{- 1 (17) + 4 w}{2 (2 - w)}$

Step 5.3.7

Factor $- 1$ out of $4 w$ .

$t = \frac{- 1 (17) - (- 4 w)}{2 (2 - w)}$

Step 5.3.8

Factor $- 1$ out of $- 1 (17) - (- 4 w)$ .

$t = \frac{- 1 (17 - 4 w)}{2 (2 - w)}$

Step 5.3.9

Move the negative in front of the fraction.

$t = - \frac{17 - 4 w}{2 (2 - w)}$