Algebra Examples

$7 (3 x + 9) = 11 - (x + 3)$

Step 1

Simplify $7 (3 x + 9)$ .

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Step 1.1

Rewrite.

$0 + 0 + 7 (3 x + 9) = 11 - (x + 3)$

Step 1.2

Simplify by adding zeros.

$7 (3 x + 9) = 11 - (x + 3)$

Step 1.3

Apply the distributive property.

$7 (3 x) + 7 \cdot 9 = 11 - (x + 3)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $7$ .

$21 x + 7 \cdot 9 = 11 - (x + 3)$

Step 1.4.2

Multiply $7$ by $9$ .

$21 x + 63 = 11 - (x + 3)$

$21 x + 63 = 11 - (x + 3)$

$21 x + 63 = 11 - (x + 3)$

Step 2

Simplify $11 - (x + 3)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$21 x + 63 = 11 - x - 1 \cdot 3$

Step 2.1.2

Multiply $- 1$ by $3$ .

$21 x + 63 = 11 - x - 3$

$21 x + 63 = 11 - x - 3$

Step 2.2

Subtract $3$ from $11$ .

$21 x + 63 = - x + 8$

$21 x + 63 = - x + 8$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Add $x$ to both sides of the equation.

$21 x + 63 + x = 8$

Step 3.2

Add $21 x$ and $x$ .

$22 x + 63 = 8$

$22 x + 63 = 8$

Step 4

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

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Step 4.1

Subtract $63$ from both sides of the equation.

$22 x = 8 - 63$

Step 4.2

Subtract $63$ from $8$ .

$22 x = - 55$

$22 x = - 55$

Step 5

Divide each term in $22 x = - 55$ by $22$ and simplify.

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Step 5.1

Divide each term in $22 x = - 55$ by $22$ .

$\frac{22 x}{22} = \frac{- 55}{22}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $22$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{22 x}{22} = \frac{- 55}{22}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 55}{22}$

$x = \frac{- 55}{22}$

$x = \frac{- 55}{22}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 55$ and $22$ .

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Step 5.3.1.1

Factor $11$ out of $- 55$ .

$x = \frac{11 (- 5)}{22}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $11$ out of $22$ .

$x = \frac{11 \cdot - 5}{11 \cdot 2}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{11 \cdot - 5}{11 \cdot 2}$

Step 5.3.1.2.3

Rewrite the expression.

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

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

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

Step 5.3.2

Move the negative in front of the fraction.

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

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 2.5$

Mixed Number Form:

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

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