Algebra Examples

$f (x) = 1.5 x + 3 (x - 4) + 4.5 (x + 9)$

Step 1

Set $1.5 x + 3 (x - 4) + 4.5 (x + 9)$ equal to $0$ .

$1.5 x + 3 (x - 4) + 4.5 (x + 9) = 0$

Step 2

Solve for $x$ .

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Step 2.1

Simplify $1.5 x + 3 (x - 4) + 4.5 (x + 9)$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$1.5 x + 3 x + 3 \cdot - 4 + 4.5 (x + 9) = 0$

Step 2.1.1.2

Multiply $3$ by $- 4$ .

$1.5 x + 3 x - 12 + 4.5 (x + 9) = 0$

Step 2.1.1.3

Apply the distributive property.

$1.5 x + 3 x - 12 + 4.5 x + 4.5 \cdot 9 = 0$

Step 2.1.1.4

Multiply $4.5$ by $9$ .

$1.5 x + 3 x - 12 + 4.5 x + 40.5 = 0$

$1.5 x + 3 x - 12 + 4.5 x + 40.5 = 0$

Step 2.1.2

Simplify by adding terms.

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Step 2.1.2.1

Add $1.5 x$ and $3 x$ .

$4.5 x - 12 + 4.5 x + 40.5 = 0$

Step 2.1.2.2

Add $4.5 x$ and $4.5 x$ .

$9 x - 12 + 40.5 = 0$

Step 2.1.2.3

Add $- 12$ and $40.5$ .

$9 x + 28.5 = 0$

$9 x + 28.5 = 0$

$9 x + 28.5 = 0$

Step 2.2

Subtract $28.5$ from both sides of the equation.

$9 x = - 28.5$

Step 2.3

Divide each term in $9 x = - 28.5$ by $9$ and simplify.

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Step 2.3.1

Divide each term in $9 x = - 28.5$ by $9$ .

$\frac{9 x}{9} = \frac{- 28.5}{9}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $9$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 28.5}{9}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 28.5}{9}$

$x = \frac{- 28.5}{9}$

$x = \frac{- 28.5}{9}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 28.5$ by $9$ .

$x = - 3.1\overline{6}$

$x = - 3.1\overline{6}$

$x = - 3.1\overline{6}$ (Multiplicity of $1$ )

$x = - 3.1\overline{6}$ (Multiplicity of $1$ )

Step 3

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