Algebra Examples

$4 + 3 x - a x = 9 - 7 x + b x$

Step 1

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

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Step 1.1

Add $7 x$ to both sides of the equation.

$4 + 3 x - a x + 7 x = 9 + b x$

Step 1.2

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

$4 + 3 x - a x + 7 x - b x = 9$

Step 1.3

Add $3 x$ and $7 x$ .

$4 - a x + 10 x - b x = 9$

Step 2

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

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Step 2.1

Subtract $4$ from both sides of the equation.

$- a x + 10 x - b x = 9 - 4$

Step 2.2

Subtract $4$ from $9$ .

$- a x + 10 x - b x = 5$

Step 3

Factor $x$ out of $- a x + 10 x - b x$ .

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Step 3.1

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

$x (- a) + 10 x - b x = 5$

Step 3.2

Factor $x$ out of $10 x$ .

$x (- a) + x \cdot 10 - b x = 5$

Step 3.3

Factor $x$ out of $- b x$ .

$x (- a) + x \cdot 10 + x (- b) = 5$

Step 3.4

Factor $x$ out of $x (- a) + x \cdot 10$ .

$x (- a + 10) + x (- b) = 5$

Step 3.5

Factor $x$ out of $x (- a + 10) + x (- b)$ .

$x (- a + 10 - b) = 5$

Step 4

Divide each term in $x (- a + 10 - b) = 5$ by $- a + 10 - b$ and simplify.

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Step 4.1

Divide each term in $x (- a + 10 - b) = 5$ by $- a + 10 - b$ .

$\frac{x (- a + 10 - b)}{- a + 10 - b} = \frac{5}{- a + 10 - b}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- a + 10 - b$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x (- a + 10 - b)}{- a + 10 - b} = \frac{5}{- a + 10 - b}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{- a + 10 - b}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Factor $- 1$ out of $- a$ .

$x = \frac{5}{- (a) + 10 - b}$

Step 4.3.2

Rewrite $10$ as $- 1 (- 10)$ .

$x = \frac{5}{- (a) - 1 (- 10) - b}$

Step 4.3.3

Factor $- 1$ out of $- (a) - 1 (- 10)$ .

$x = \frac{5}{- (a - 10) - b}$

Step 4.3.4

Factor $- 1$ out of $- b$ .

$x = \frac{5}{- (a - 10) - (b)}$

Step 4.3.5

Factor $- 1$ out of $- (a - 10) - (b)$ .

$x = \frac{5}{- (a - 10 + b)}$

Step 4.3.6

Rewrite negatives.

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Step 4.3.6.1

Rewrite $- (a - 10 + b)$ as $- 1 (a - 10 + b)$ .

$x = \frac{5}{- 1 (a - 10 + b)}$

Step 4.3.6.2

Move the negative in front of the fraction.

$x = - \frac{5}{a - 10 + b}$