Algebra Examples

$3 x = (2 x - 1) (m + 4)$

Step 1

Simplify $(2 x - 1) (m + 4)$ .

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Step 1.1

Expand $(2 x - 1) (m + 4)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$3 x = 2 x (m + 4) - 1 (m + 4)$

Step 1.1.2

Apply the distributive property.

$3 x = 2 x m + 2 x \cdot 4 - 1 (m + 4)$

Step 1.1.3

Apply the distributive property.

$3 x = 2 x m + 2 x \cdot 4 - 1 m - 1 \cdot 4$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $4$ by $2$ .

$3 x = 2 x m + 8 x - 1 m - 1 \cdot 4$

Step 1.2.2

Rewrite $- 1 m$ as $- m$ .

$3 x = 2 x m + 8 x - m - 1 \cdot 4$

Step 1.2.3

Multiply $- 1$ by $4$ .

$3 x = 2 x m + 8 x - m - 4$

Step 2

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

$2 x m + 8 x - m - 4 = 3 x$

Step 3

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

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Step 3.1

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

$2 x m + 8 x - m - 4 - 3 x = 0$

Step 3.2

Subtract $3 x$ from $8 x$ .

$2 x m + 5 x - m - 4 = 0$

Step 4

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

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Step 4.1

Add $m$ to both sides of the equation.

$2 x m + 5 x - 4 = m$

Step 4.2

Add $4$ to both sides of the equation.

$2 x m + 5 x = m + 4$

Step 5

Factor $x$ out of $2 x m + 5 x$ .

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Step 5.1

Factor $x$ out of $2 x m$ .

$x (2 m) + 5 x = m + 4$

Step 5.2

Factor $x$ out of $5 x$ .

$x (2 m) + x \cdot 5 = m + 4$

Step 5.3

Factor $x$ out of $x (2 m) + x \cdot 5$ .

$x (2 m + 5) = m + 4$

Step 6

Divide each term in $x (2 m + 5) = m + 4$ by $2 m + 5$ and simplify.

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Step 6.1

Divide each term in $x (2 m + 5) = m + 4$ by $2 m + 5$ .

$\frac{x (2 m + 5)}{2 m + 5} = \frac{m}{2 m + 5} + \frac{4}{2 m + 5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2 m + 5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{x (2 m + 5)}{2 m + 5} = \frac{m}{2 m + 5} + \frac{4}{2 m + 5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{m}{2 m + 5} + \frac{4}{2 m + 5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Combine the numerators over the common denominator.

$x = \frac{m + 4}{2 m + 5}$