Solve for x -6/5(4-x)<=-4(x+1/2)

$- \frac{6}{5} (4 - x) \leq - 4 (x + \frac{1}{2})$

Step 1

Simplify $- \frac{6}{5} \cdot (4 - x)$ .

Start simplifying.

$0 + 0 - \frac{6}{5} \cdot (4 - x) \leq - 4 (x + \frac{1}{2})$

Simplify by adding zeros.

$- \frac{6}{5} \cdot (4 - x) \leq - 4 (x + \frac{1}{2})$

Apply the distributive property.

$- \frac{6}{5} \cdot 4 - \frac{6}{5} (- x) \leq - 4 (x + \frac{1}{2})$

Multiply $- \frac{6}{5} \cdot 4$ .

Multiply $4$ by $- 1$ .

$- 4 (\frac{6}{5}) - \frac{6}{5} (- x) \leq - 4 (x + \frac{1}{2})$

Combine $- 4$ and $\frac{6}{5}$ .

$\frac{- 4 \cdot 6}{5} - \frac{6}{5} (- x) \leq - 4 (x + \frac{1}{2})$

Multiply $- 4$ by $6$ .

$\frac{- 24}{5} - \frac{6}{5} (- x) \leq - 4 (x + \frac{1}{2})$

Multiply $- \frac{6}{5} (- x)$ .

Multiply $- 1$ by $- 1$ .

$\frac{- 24}{5} + 1 (\frac{6}{5}) x \leq - 4 (x + \frac{1}{2})$

Multiply $\frac{6}{5}$ by $1$ .

$\frac{- 24}{5} + \frac{6}{5} x \leq - 4 (x + \frac{1}{2})$

Combine $\frac{6}{5}$ and $x$ .

$\frac{- 24}{5} + \frac{6 x}{5} \leq - 4 (x + \frac{1}{2})$

Move the negative in front of the fraction.

$- \frac{24}{5} + \frac{6 x}{5} \leq - 4 (x + \frac{1}{2})$

Step 2

Simplify $- 4 (x + \frac{1}{2})$ .

Apply the distributive property.

$- \frac{24}{5} + \frac{6 x}{5} \leq - 4 x - 4 (\frac{1}{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$- \frac{24}{5} + \frac{6 x}{5} \leq - 4 x + 2 (- 2) \frac{1}{2}$

Cancel the common factor.

$- \frac{24}{5} + \frac{6 x}{5} \leq - 4 x + 2 \cdot - 2 \frac{1}{2}$

Rewrite the expression.

$- \frac{24}{5} + \frac{6 x}{5} \leq - 4 x - 2$

Step 3

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

Add $4 x$ to both sides of the inequality.

$- \frac{24}{5} + \frac{6 x}{5} + 4 x \leq - 2$

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{24}{5} + \frac{6 x}{5} + 4 x \cdot \frac{5}{5} \leq - 2$

Combine $4 x$ and $\frac{5}{5}$ .

$- \frac{24}{5} + \frac{6 x}{5} + \frac{4 x \cdot 5}{5} \leq - 2$

Combine the numerators over the common denominator.

$- \frac{24}{5} + \frac{6 x + 4 x \cdot 5}{5} \leq - 2$

Combine the numerators over the common denominator.

$\frac{- 24 + 6 x + 4 x \cdot 5}{5} \leq - 2$

Multiply $5$ by $4$ .

$\frac{- 24 + 6 x + 20 x}{5} \leq - 2$

Add $6 x$ and $20 x$ .

$\frac{- 24 + 26 x}{5} \leq - 2$

Factor $2$ out of $- 24 + 26 x$ .

Factor $2$ out of $- 24$ .

$\frac{2 (- 12) + 26 x}{5} \leq - 2$

Factor $2$ out of $26 x$ .

$\frac{2 (- 12) + 2 (13 x)}{5} \leq - 2$

Factor $2$ out of $2 (- 12) + 2 (13 x)$ .

$\frac{2 (- 12 + 13 x)}{5} \leq - 2$

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{2 (- 1 (12) + 13 x)}{5} \leq - 2$

Factor $- 1$ out of $13 x$ .

$\frac{2 (- 1 (12) - (- 13 x))}{5} \leq - 2$

Factor $- 1$ out of $- 1 (12) - (- 13 x)$ .

$\frac{2 (- 1 (12 - 13 x))}{5} \leq - 2$

Move the negative in front of the fraction.

$- \frac{2 (12 - 13 x)}{5} \leq - 2$

Step 4

Divide each term in $- \frac{2 (12 - 13 x)}{5} \leq - 2$ by $- 1$ and simplify.

Divide each term in $- \frac{2 (12 - 13 x)}{5} \leq - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{2 (12 - 13 x)}{5}}{- 1} \geq \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{2 (12 - 13 x)}{5}}{1} \geq \frac{- 2}{- 1}$

Divide $\frac{2 (12 - 13 x)}{5}$ by $1$ .

$\frac{2 (12 - 13 x)}{5} \geq \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$\frac{2 (12 - 13 x)}{5} \geq 2$

Step 5

Multiply both sides by $5$ .

$\frac{2 (12 - 13 x)}{5} \cdot 5 \geq 2 \cdot 5$

Step 6

Simplify.

Simplify the left side.

Simplify $\frac{2 (12 - 13 x)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 (12 - 13 x)}{5} \cdot 5 \geq 2 \cdot 5$

Rewrite the expression.

$2 (12 - 13 x) \geq 2 \cdot 5$

Apply the distributive property.

$2 \cdot 12 + 2 (- 13 x) \geq 2 \cdot 5$

Simplify the expression.

Multiply $2$ by $12$ .

$24 + 2 (- 13 x) \geq 2 \cdot 5$

Multiply $- 13$ by $2$ .

$24 - 26 x \geq 2 \cdot 5$

Reorder $24$ and $- 26 x$ .

$- 26 x + 24 \geq 2 \cdot 5$

Simplify the right side.

Multiply $2$ by $5$ .

$- 26 x + 24 \geq 10$

Step 7

Solve for $x$ .

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

Subtract $24$ from both sides of the inequality.

$- 26 x \geq 10 - 24$

Subtract $24$ from $10$ .

$- 26 x \geq - 14$

Divide each term in $- 26 x \geq - 14$ by $- 26$ and simplify.

Divide each term in $- 26 x \geq - 14$ by $- 26$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 26 x}{- 26} \leq \frac{- 14}{- 26}$

Simplify the left side.

Cancel the common factor of $- 26$ .

Cancel the common factor.

$\frac{- 26 x}{- 26} \leq \frac{- 14}{- 26}$

Divide $x$ by $1$ .

$x \leq \frac{- 14}{- 26}$

Simplify the right side.

Cancel the common factor of $- 14$ and $- 26$ .

Factor $- 2$ out of $- 14$ .

$x \leq \frac{- 2 (7)}{- 26}$

Cancel the common factors.

Factor $- 2$ out of $- 26$ .

$x \leq \frac{- 2 \cdot 7}{- 2 \cdot 13}$

Cancel the common factor.

$x \leq \frac{- 2 \cdot 7}{- 2 \cdot 13}$

Rewrite the expression.

$x \leq \frac{7}{13}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{7}{13}$

Interval Notation:

$(- \infty, \frac{7}{13}]$

Solve for x -6/5(4-x)<=-4(x+1/2)

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