Pre-Algebra Examples

$\frac{8 (x + 2)}{3} = 3 x + 8$

Step 1

Multiply both sides by $3$ .

$\frac{8 (x + 2)}{3} \cdot 3 = (3 x + 8) \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{8 (x + 2)}{3} \cdot 3$ .

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Step 2.1.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{8 (x + 2)}{3} \cdot 3 = (3 x + 8) \cdot 3$

Step 2.1.1.1.2

Rewrite the expression.

$8 (x + 2) = (3 x + 8) \cdot 3$

Step 2.1.1.2

Apply the distributive property.

$8 x + 8 \cdot 2 = (3 x + 8) \cdot 3$

Step 2.1.1.3

Multiply $8$ by $2$ .

$8 x + 16 = (3 x + 8) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(3 x + 8) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$8 x + 16 = 3 x \cdot 3 + 8 \cdot 3$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $3$ by $3$ .

$8 x + 16 = 9 x + 8 \cdot 3$

Step 2.2.1.2.2

Multiply $8$ by $3$ .

$8 x + 16 = 9 x + 24$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $9 x$ from both sides of the equation.

$8 x + 16 - 9 x = 24$

Step 3.1.2

Subtract $9 x$ from $8 x$ .

$- x + 16 = 24$

Step 3.2

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

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Step 3.2.1

Subtract $16$ from both sides of the equation.

$- x = 24 - 16$

Step 3.2.2

Subtract $16$ from $24$ .

$- x = 8$

Step 3.3

Divide each term in $- x = 8$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- x = 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{8}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{8}{- 1}$

Step 3.3.2.2

Divide $x$ by $1$ .

$x = \frac{8}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $8$ by $- 1$ .

$x = - 8$