Algebra Examples

$\frac{2 x}{3} + \frac{16}{3} = - \frac{4 x}{2}$

Step 1

Cancel the common factor of $4$ and $2$ .

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Step 1.1

Factor $2$ out of $4 x$ .

$\frac{2 x}{3} + \frac{16}{3} = - \frac{2 (2 x)}{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

$\frac{2 x}{3} + \frac{16}{3} = - \frac{2 (2 x)}{2 (1)}$

Step 1.2.2

Cancel the common factor.

$\frac{2 x}{3} + \frac{16}{3} = - \frac{2 (2 x)}{2 \cdot 1}$

Step 1.2.3

Rewrite the expression.

$\frac{2 x}{3} + \frac{16}{3} = - \frac{2 x}{1}$

Step 1.2.4

Divide $2 x$ by $1$ .

$\frac{2 x}{3} + \frac{16}{3} = - (2 x)$

Step 2

Solve for $x$ .

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Step 2.1

Multiply $2$ by $- 1$ .

$\frac{2 x}{3} + \frac{16}{3} = - 2 x$

Step 2.2

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

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Step 2.2.1

Add $2 x$ to both sides of the equation.

$\frac{2 x}{3} + \frac{16}{3} + 2 x = 0$

Step 2.2.2

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3} + 2 x \cdot \frac{3}{3} + \frac{16}{3} = 0$

Step 2.2.3

Combine $2 x$ and $\frac{3}{3}$ .

$\frac{2 x}{3} + \frac{2 x \cdot 3}{3} + \frac{16}{3} = 0$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{2 x + 2 x \cdot 3}{3} + \frac{16}{3} = 0$

Step 2.2.5

Combine the numerators over the common denominator.

$\frac{2 x + 2 x \cdot 3 + 16}{3} = 0$

Step 2.2.6

Multiply $3$ by $2$ .

$\frac{2 x + 6 x + 16}{3} = 0$

Step 2.2.7

Add $2 x$ and $6 x$ .

$\frac{8 x + 16}{3} = 0$

Step 2.2.8

Factor $8$ out of $8 x + 16$ .

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Step 2.2.8.1

Factor $8$ out of $8 x$ .

$\frac{8 (x) + 16}{3} = 0$

Step 2.2.8.2

Factor $8$ out of $16$ .

$\frac{8 x + 8 \cdot 2}{3} = 0$

Step 2.2.8.3

Factor $8$ out of $8 x + 8 \cdot 2$ .

$\frac{8 (x + 2)}{3} = 0$

Step 2.3

Set the numerator equal to zero.

$8 (x + 2) = 0$

Step 2.4

Solve the equation for $x$ .

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Step 2.4.1

Divide each term in $8 (x + 2) = 0$ by $8$ and simplify.

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Step 2.4.1.1

Divide each term in $8 (x + 2) = 0$ by $8$ .

$\frac{8 (x + 2)}{8} = \frac{0}{8}$

Step 2.4.1.2

Simplify the left side.

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Step 2.4.1.2.1

Cancel the common factor of $8$ .

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Step 2.4.1.2.1.1

Cancel the common factor.

$\frac{8 (x + 2)}{8} = \frac{0}{8}$

Step 2.4.1.2.1.2

Divide $x + 2$ by $1$ .

$x + 2 = \frac{0}{8}$

Step 2.4.1.3

Simplify the right side.

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Step 2.4.1.3.1

Divide $0$ by $8$ .

$x + 2 = 0$

Step 2.4.2

Subtract $2$ from both sides of the equation.

$x = - 2$