Algebra Examples

$8 x - 8 + 3 a x = 5 a x - 2 a$

Step 1

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$5 a x - 2 a = 8 x - 8 + 3 a x$

Step 2

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

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Step 2.1

Subtract $3 a x$ from both sides of the equation.

$5 a x - 2 a - 3 a x = 8 x - 8$

Step 2.2

Subtract $3 a x$ from $5 a x$ .

$- 2 a + 2 a x = 8 x - 8$

Step 3

Factor $2 a$ out of $- 2 a + 2 a x$ .

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Step 3.1

Factor $2 a$ out of $- 2 a$ .

$2 a (- 1) + 2 a x = 8 x - 8$

Step 3.2

Factor $2 a$ out of $2 a x$ .

$2 a (- 1) + 2 a (x) = 8 x - 8$

Step 3.3

Factor $2 a$ out of $2 a (- 1) + 2 a (x)$ .

$2 a (- 1 + x) = 8 x - 8$

Step 4

Divide each term in $2 a (- 1 + x) = 8 x - 8$ by $2 (- 1 + x)$ and simplify.

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Step 4.1

Divide each term in $2 a (- 1 + x) = 8 x - 8$ by $2 (- 1 + x)$ .

$\frac{2 a (- 1 + x)}{2 (- 1 + x)} = \frac{8 x}{2 (- 1 + x)} + \frac{- 8}{2 (- 1 + x)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 a (- 1 + x)}{2 (- 1 + x)} = \frac{8 x}{2 (- 1 + x)} + \frac{- 8}{2 (- 1 + x)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{a (- 1 + x)}{- 1 + x} = \frac{8 x}{2 (- 1 + x)} + \frac{- 8}{2 (- 1 + x)}$

Step 4.2.2

Cancel the common factor of $- 1 + x$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{a (- 1 + x)}{- 1 + x} = \frac{8 x}{2 (- 1 + x)} + \frac{- 8}{2 (- 1 + x)}$

Step 4.2.2.2

Divide $a$ by $1$ .

$a = \frac{8 x}{2 (- 1 + x)} + \frac{- 8}{2 (- 1 + x)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $8$ and $2$ .

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Step 4.3.1.1.1

Factor $2$ out of $8 x$ .

$a = \frac{2 (4 x)}{2 (- 1 + x)} + \frac{- 8}{2 (- 1 + x)}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Cancel the common factor.

$a = \frac{2 (4 x)}{2 (- 1 + x)} + \frac{- 8}{2 (- 1 + x)}$

Step 4.3.1.1.2.2

Rewrite the expression.

$a = \frac{4 x}{- 1 + x} + \frac{- 8}{2 (- 1 + x)}$

Step 4.3.1.2

Cancel the common factor of $- 8$ and $2$ .

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Step 4.3.1.2.1

Factor $2$ out of $- 8$ .

$a = \frac{4 x}{- 1 + x} + \frac{2 \cdot - 4}{2 (- 1 + x)}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Cancel the common factor.

$a = \frac{4 x}{- 1 + x} + \frac{2 \cdot - 4}{2 (- 1 + x)}$

Step 4.3.1.2.2.2

Rewrite the expression.

$a = \frac{4 x}{- 1 + x} + \frac{- 4}{- 1 + x}$

Step 4.3.1.3

Move the negative in front of the fraction.

$a = \frac{4 x}{- 1 + x} - \frac{4}{- 1 + x}$

Step 4.3.2

Simplify terms.

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Step 4.3.2.1

Combine the numerators over the common denominator.

$a = \frac{4 x - 4}{- 1 + x}$

Step 4.3.2.2

Factor $4$ out of $4 x - 4$ .

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Step 4.3.2.2.1

Factor $4$ out of $4 x$ .

$a = \frac{4 (x) - 4}{- 1 + x}$

Step 4.3.2.2.2

Factor $4$ out of $- 4$ .

$a = \frac{4 (x) + 4 (- 1)}{- 1 + x}$

Step 4.3.2.2.3

Factor $4$ out of $4 (x) + 4 (- 1)$ .

$a = \frac{4 (x - 1)}{- 1 + x}$

Step 4.3.2.3

Cancel the common factor of $x - 1$ and $- 1 + x$ .

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Step 4.3.2.3.1

Reorder terms.

$a = \frac{4 (x - 1)}{x - 1}$

Step 4.3.2.3.2

Cancel the common factor.

$a = \frac{4 (x - 1)}{x - 1}$

Step 4.3.2.3.3

Divide $4$ by $1$ .

$a = 4$