Algebra Examples

$8 (4 x + 6) = 11 - (x + 7)$

Step 1

Simplify $8 (4 x + 6)$ .

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Step 1.1

Rewrite.

$0 + 0 + 8 (4 x + 6) = 11 - (x + 7)$

Step 1.2

Simplify by adding zeros.

$8 (4 x + 6) = 11 - (x + 7)$

Step 1.3

Apply the distributive property.

$8 (4 x) + 8 \cdot 6 = 11 - (x + 7)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $4$ by $8$ .

$32 x + 8 \cdot 6 = 11 - (x + 7)$

Step 1.4.2

Multiply $8$ by $6$ .

$32 x + 48 = 11 - (x + 7)$

$32 x + 48 = 11 - (x + 7)$

$32 x + 48 = 11 - (x + 7)$

Step 2

Simplify $11 - (x + 7)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$32 x + 48 = 11 - x - 1 \cdot 7$

Step 2.1.2

Multiply $- 1$ by $7$ .

$32 x + 48 = 11 - x - 7$

$32 x + 48 = 11 - x - 7$

Step 2.2

Subtract $7$ from $11$ .

$32 x + 48 = - x + 4$

$32 x + 48 = - x + 4$

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.

$32 x + 48 + x = 4$

Step 3.2

Add $32 x$ and $x$ .

$33 x + 48 = 4$

$33 x + 48 = 4$

Step 4

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

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Step 4.1

Subtract $48$ from both sides of the equation.

$33 x = 4 - 48$

Step 4.2

Subtract $48$ from $4$ .

$33 x = - 44$

$33 x = - 44$

Step 5

Divide each term in $33 x = - 44$ by $33$ and simplify.

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Step 5.1

Divide each term in $33 x = - 44$ by $33$ .

$\frac{33 x}{33} = \frac{- 44}{33}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $33$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{33 x}{33} = \frac{- 44}{33}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 44}{33}$

$x = \frac{- 44}{33}$

$x = \frac{- 44}{33}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 44$ and $33$ .

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Step 5.3.1.1

Factor $11$ out of $- 44$ .

$x = \frac{11 (- 4)}{33}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $11$ out of $33$ .

$x = \frac{11 \cdot - 4}{11 \cdot 3}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{11 \cdot - 4}{11 \cdot 3}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{- 4}{3}$

$x = \frac{- 4}{3}$

$x = \frac{- 4}{3}$

Step 5.3.2

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

$x = - \frac{4}{3}$

$x = - \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

$x = - 1 \frac{1}{3}$

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