Algebra Examples

$6 x + 3 = m (2 x + 1)$

Step 1

Rewrite the equation as $m (2 x + 1) = 6 x + 3$ .

$m (2 x + 1) = 6 x + 3$

Step 2

Divide each term in $m (2 x + 1) = 6 x + 3$ by $2 x + 1$ and simplify.

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Step 2.1

Divide each term in $m (2 x + 1) = 6 x + 3$ by $2 x + 1$ .

$\frac{m (2 x + 1)}{2 x + 1} = \frac{6 x}{2 x + 1} + \frac{3}{2 x + 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2 x + 1$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{m (2 x + 1)}{2 x + 1} = \frac{6 x}{2 x + 1} + \frac{3}{2 x + 1}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m = \frac{6 x}{2 x + 1} + \frac{3}{2 x + 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine the numerators over the common denominator.

$m = \frac{6 x + 3}{2 x + 1}$

Step 2.3.2

Factor $3$ out of $6 x + 3$ .

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Step 2.3.2.1

Factor $3$ out of $6 x$ .

$m = \frac{3 (2 x) + 3}{2 x + 1}$

Step 2.3.2.2

Factor $3$ out of $3$ .

$m = \frac{3 (2 x) + 3 (1)}{2 x + 1}$

Step 2.3.2.3

Factor $3$ out of $3 (2 x) + 3 (1)$ .

$m = \frac{3 (2 x + 1)}{2 x + 1}$

Step 2.3.3

Cancel the common factor of $2 x + 1$ .

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Step 2.3.3.1

Cancel the common factor.

$m = \frac{3 (2 x + 1)}{2 x + 1}$

Step 2.3.3.2

Divide $3$ by $1$ .

$m = 3$