Finite Math Examples

$(4 - w) (3 w - 7) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$4 - w = 0$

$3 w - 7 = 0$

Step 2

Set $4 - w$ equal to $0$ and solve for $w$ .

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Step 2.1

Set $4 - w$ equal to $0$ .

$4 - w = 0$

Step 2.2

Solve $4 - w = 0$ for $w$ .

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Step 2.2.1

Subtract $4$ from both sides of the equation.

$- w = - 4$

Step 2.2.2

Divide each term in $- w = - 4$ by $- 1$ and simplify.

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Step 2.2.2.1

Divide each term in $- w = - 4$ by $- 1$ .

$\frac{- w}{- 1} = \frac{- 4}{- 1}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{w}{1} = \frac{- 4}{- 1}$

Step 2.2.2.2.2

Divide $w$ by $1$ .

$w = \frac{- 4}{- 1}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide $- 4$ by $- 1$ .

$w = 4$

Step 3

Set $3 w - 7$ equal to $0$ and solve for $w$ .

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Step 3.1

Set $3 w - 7$ equal to $0$ .

$3 w - 7 = 0$

Step 3.2

Solve $3 w - 7 = 0$ for $w$ .

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Step 3.2.1

Add $7$ to both sides of the equation.

$3 w = 7$

Step 3.2.2

Divide each term in $3 w = 7$ by $3$ and simplify.

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Step 3.2.2.1

Divide each term in $3 w = 7$ by $3$ .

$\frac{3 w}{3} = \frac{7}{3}$

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{3 w}{3} = \frac{7}{3}$

Step 3.2.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{7}{3}$

Step 4

The final solution is all the values that make $(4 - w) (3 w - 7) = 0$ true.

$w = 4, \frac{7}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = 4, \frac{7}{3}$

Decimal Form:

$w = 4, 2.\overline{3}$

Mixed Number Form:

$w = 4, 2 \frac{1}{3}$