Pre-Algebra Examples

$(9 x - 8) (2 x + 1) = 0$

Step 1

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

$9 x - 8 = 0$

$2 x + 1 = 0$

Step 2

Set $9 x - 8$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $9 x - 8$ equal to $0$ .

$9 x - 8 = 0$

Step 2.2

Solve $9 x - 8 = 0$ for $x$ .

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Step 2.2.1

Add $8$ to both sides of the equation.

$9 x = 8$

Step 2.2.2

Divide each term in $9 x = 8$ by $9$ and simplify.

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Step 2.2.2.1

Divide each term in $9 x = 8$ by $9$ .

$\frac{9 x}{9} = \frac{8}{9}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $9$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{8}{9}$

Step 2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{9}$

Step 3

Set $2 x + 1$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Step 3.2

Solve $2 x + 1 = 0$ for $x$ .

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Step 3.2.1

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Step 3.2.2

Divide each term in $2 x = - 1$ by $2$ and simplify.

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Step 3.2.2.1

Divide each term in $2 x = - 1$ by $2$ .

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

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 3.2.2.3

Simplify the right side.

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Step 3.2.2.3.1

Move the negative in front of the fraction.

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

Step 4

The final solution is all the values that make $(9 x - 8) (2 x + 1) = 0$ true.

$x = \frac{8}{9}, - \frac{1}{2}$