Solve the Inequality for x 2x<=-2/3(4x+4)

$2 x \leq - \frac{2}{3} (4 x + 4)$

Step 1

Simplify $- \frac{2}{3} \cdot (4 x + 4)$ .

Apply the distributive property.

$2 x \leq - \frac{2}{3} (4 x) - \frac{2}{3} \cdot 4$

Multiply $- \frac{2}{3} (4 x)$ .

Multiply $4$ by $- 1$ .

$2 x \leq - 4 (\frac{2}{3}) x - \frac{2}{3} \cdot 4$

Combine $- 4$ and $\frac{2}{3}$ .

$2 x \leq \frac{- 4 \cdot 2}{3} x - \frac{2}{3} \cdot 4$

Multiply $- 4$ by $2$ .

$2 x \leq \frac{- 8}{3} x - \frac{2}{3} \cdot 4$

Combine $\frac{- 8}{3}$ and $x$ .

$2 x \leq \frac{- 8 x}{3} - \frac{2}{3} \cdot 4$

Multiply $- \frac{2}{3} \cdot 4$ .

Multiply $4$ by $- 1$ .

$2 x \leq \frac{- 8 x}{3} - 4 (\frac{2}{3})$

Combine $- 4$ and $\frac{2}{3}$ .

$2 x \leq \frac{- 8 x}{3} + \frac{- 4 \cdot 2}{3}$

Multiply $- 4$ by $2$ .

$2 x \leq \frac{- 8 x}{3} + \frac{- 8}{3}$

Simplify each term.

Move the negative in front of the fraction.

$2 x \leq - \frac{(8) x}{3} + \frac{- 8}{3}$

Move the negative in front of the fraction.

$2 x \leq - \frac{8 x}{3} - \frac{8}{3}$

Step 2

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

Add $\frac{8 x}{3}$ to both sides of the inequality.

$2 x + \frac{8 x}{3} \leq - \frac{8}{3}$

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

$2 x \cdot \frac{3}{3} + \frac{8 x}{3} \leq - \frac{8}{3}$

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

$\frac{2 x \cdot 3}{3} + \frac{8 x}{3} \leq - \frac{8}{3}$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 + 8 x}{3} \leq - \frac{8}{3}$

Simplify the numerator.

Factor $2 x$ out of $2 x \cdot 3 + 8 x$ .

Factor $2 x$ out of $2 x \cdot 3$ .

$\frac{2 x (3) + 8 x}{3} \leq - \frac{8}{3}$

Factor $2 x$ out of $8 x$ .

$\frac{2 x (3) + 2 x (4)}{3} \leq - \frac{8}{3}$

Factor $2 x$ out of $2 x (3) + 2 x (4)$ .

$\frac{2 x (3 + 4)}{3} \leq - \frac{8}{3}$

Add $3$ and $4$ .

$\frac{2 x \cdot 7}{3} \leq - \frac{8}{3}$

Multiply $7$ by $2$ .

$\frac{14 x}{3} \leq - \frac{8}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$14 x \leq - 8$

Step 4

Divide each term in $14 x \leq - 8$ by $14$ and simplify.

Divide each term in $14 x \leq - 8$ by $14$ .

$\frac{14 x}{14} \leq \frac{- 8}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} \leq \frac{- 8}{14}$

Divide $x$ by $1$ .

$x \leq \frac{- 8}{14}$

Simplify the right side.

Cancel the common factor of $- 8$ and $14$ .

Factor $2$ out of $- 8$ .

$x \leq \frac{2 (- 4)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$x \leq \frac{2 \cdot - 4}{2 \cdot 7}$

Cancel the common factor.

$x \leq \frac{2 \cdot - 4}{2 \cdot 7}$

Rewrite the expression.

$x \leq \frac{- 4}{7}$

Move the negative in front of the fraction.

$x \leq - \frac{4}{7}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{4}{7}$

Interval Notation:

$(- \infty, - \frac{4}{7}]$

Solve the Inequality for x 2x<=-2/3(4x+4)

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