Solve the Inequality for x 6(-1/2x-1/3)<=10

$6 (- \frac{1}{2} x - \frac{1}{3}) \leq 10$

Step 1

Simplify.

Combine $x$ and $\frac{1}{2}$ .

$6 (- \frac{x}{2} - \frac{1}{3}) \leq 10$

Apply the distributive property.

$6 (- \frac{x}{2}) + 6 (- \frac{1}{3}) \leq 10$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$6 \frac{- x}{2} + 6 (- \frac{1}{3}) \leq 10$

Factor $2$ out of $6$ .

$2 (3) \frac{- x}{2} + 6 (- \frac{1}{3}) \leq 10$

Cancel the common factor.

$2 \cdot 3 \frac{- x}{2} + 6 (- \frac{1}{3}) \leq 10$

Rewrite the expression.

$3 (- x) + 6 (- \frac{1}{3}) \leq 10$

Multiply $- 1$ by $3$ .

$- 3 x + 6 (- \frac{1}{3}) \leq 10$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$- 3 x + 6 (\frac{- 1}{3}) \leq 10$

Factor $3$ out of $6$ .

$- 3 x + 3 (2) \frac{- 1}{3} \leq 10$

Cancel the common factor.

$- 3 x + 3 \cdot 2 \frac{- 1}{3} \leq 10$

Rewrite the expression.

$- 3 x + 2 \cdot - 1 \leq 10$

Multiply $2$ by $- 1$ .

$- 3 x - 2 \leq 10$

Step 2

Divide each term in $(- 3 x - 2) \leq 10$ by $6$ and simplify.

Divide each term in $(- 3 x - 2) \leq 10$ by $6$ .

$\frac{(- 3 x - 2)}{6} \leq \frac{10}{6}$

Simplify the left side.

Factor $- 1$ out of $- 3 x$ .

$\frac{- (3 x) - 2}{6} \leq \frac{10}{6}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- (3 x) - 1 (2)}{6} \leq \frac{10}{6}$

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

$\frac{- (3 x + 2)}{6} \leq \frac{10}{6}$

Simplify the expression.

Rewrite $- (3 x + 2)$ as $- 1 (3 x + 2)$ .

$\frac{- 1 (3 x + 2)}{6} \leq \frac{10}{6}$

Move the negative in front of the fraction.

$- \frac{3 x + 2}{6} \leq \frac{10}{6}$

Simplify the right side.

Cancel the common factor of $10$ and $6$ .

Factor $2$ out of $10$ .

$- \frac{3 x + 2}{6} \leq \frac{2 (5)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$- \frac{3 x + 2}{6} \leq \frac{2 \cdot 5}{2 \cdot 3}$

Cancel the common factor.

$- \frac{3 x + 2}{6} \leq \frac{2 \cdot 5}{2 \cdot 3}$

Rewrite the expression.

$- \frac{3 x + 2}{6} \leq \frac{5}{3}$

Step 3

Divide each term in $- \frac{3 x + 2}{6} \leq \frac{5}{3}$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x + 2}{6} \leq \frac{5}{3}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x + 2}{6}}{- 1} \geq \frac{\frac{5}{3}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 x + 2}{6}}{1} \geq \frac{\frac{5}{3}}{- 1}$

Divide $\frac{3 x + 2}{6}$ by $1$ .

$\frac{3 x + 2}{6} \geq \frac{\frac{5}{3}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{5}{3}}{- 1}$ .

$\frac{3 x + 2}{6} \geq - 1 \cdot \frac{5}{3}$

Rewrite $- 1 \cdot \frac{5}{3}$ as $- \frac{5}{3}$ .

$\frac{3 x + 2}{6} \geq - \frac{5}{3}$

Step 4

Multiply both sides by $6$ .

$\frac{3 x + 2}{6} \cdot 6 \geq - \frac{5}{3} \cdot 6$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{3 x + 2}{6} \cdot 6 \geq - \frac{5}{3} \cdot 6$

Rewrite the expression.

$3 x + 2 \geq - \frac{5}{3} \cdot 6$

Simplify the right side.

Simplify $- \frac{5}{3} \cdot 6$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$3 x + 2 \geq \frac{- 5}{3} \cdot 6$

Factor $3$ out of $6$ .

$3 x + 2 \geq \frac{- 5}{3} \cdot (3 (2))$

Cancel the common factor.

$3 x + 2 \geq \frac{- 5}{3} \cdot (3 \cdot 2)$

Rewrite the expression.

$3 x + 2 \geq - 5 \cdot 2$

Multiply $- 5$ by $2$ .

$3 x + 2 \geq - 10$

Step 6

Solve for $x$ .

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

Subtract $2$ from both sides of the inequality.

$3 x \geq - 10 - 2$

Subtract $2$ from $- 10$ .

$3 x \geq - 12$

Divide each term in $3 x \geq - 12$ by $3$ and simplify.

Divide each term in $3 x \geq - 12$ by $3$ .

$\frac{3 x}{3} \geq \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{- 12}{3}$

Divide $x$ by $1$ .

$x \geq \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$x \geq - 4$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 4$

Interval Notation:

$[- 4, \infty)$

Solve the Inequality for x 6(-1/2x-1/3)<=10

Related Questions

Support LCMGCF.com by disabling your adblocker.