Solve the System of Inequalities -x-6<=-3 or -4x+3>-1

$- x - 6 \leq - 3$ or $- 4 x + 3 > - 1$

Simplify the first inequality.

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

Add $6$ to both sides of the inequality.

$- x \leq - 3 + 6$ or $- 4 x + 3 > - 1$

Add $- 3$ and $6$ .

$- x \leq 3$ or $- 4 x + 3 > - 1$

Divide each term in $- x \leq 3$ by $- 1$ and simplify.

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

$\frac{- x}{- 1} \geq \frac{3}{- 1}$ or $- 4 x + 3 > - 1$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{3}{- 1}$ or $- 4 x + 3 > - 1$

Divide $x$ by $1$ .

$x \geq \frac{3}{- 1}$ or $- 4 x + 3 > - 1$

Simplify the right side.

Divide $3$ by $- 1$ .

$x \geq - 3$ or $- 4 x + 3 > - 1$

Simplify the second inequality.

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

Subtract $3$ from both sides of the inequality.

$x \geq - 3$ or $- 4 x > - 1 - 3$

Subtract $3$ from $- 1$ .

$x \geq - 3$ or $- 4 x > - 4$

Divide each term in $- 4 x > - 4$ by $- 4$ and simplify.

Divide each term in $- 4 x > - 4$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \geq - 3$ or $\frac{- 4 x}{- 4} < \frac{- 4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$x \geq - 3$ or $\frac{- 4 x}{- 4} < \frac{- 4}{- 4}$

Divide $x$ by $1$ .

$x \geq - 3$ or $x < \frac{- 4}{- 4}$

Simplify the right side.

Divide $- 4$ by $- 4$ .

$x \geq - 3$ or $x < 1$

The union consists of all of the elements that are contained in each interval.

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Solve the System of Inequalities -x-6<=-3 or -4x+3>-1

Related Questions

Support LCMGCF.com by disabling your adblocker.