Solve the System of Inequalities -4x+3>-9 and -6x<=12

$- 4 x + 3 > - 9$ and $- 6 x \leq 12$

Simplify the first inequality.

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

Subtract $3$ from both sides of the inequality.

$- 4 x > - 9 - 3$ and $- 6 x \leq 12$

Subtract $3$ from $- 9$ .

$- 4 x > - 12$ and $- 6 x \leq 12$

Divide each term in $- 4 x > - 12$ by $- 4$ and simplify.

Divide each term in $- 4 x > - 12$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{- 12}{- 4}$ and $- 6 x \leq 12$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{- 12}{- 4}$ and $- 6 x \leq 12$

Divide $x$ by $1$ .

$x < \frac{- 12}{- 4}$ and $- 6 x \leq 12$

Simplify the right side.

Divide $- 12$ by $- 4$ .

$x < 3$ and $- 6 x \leq 12$

Divide each term in $- 6 x \leq 12$ by $- 6$ and simplify.

Divide each term in $- 6 x \leq 12$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < 3$ and $\frac{- 6 x}{- 6} \geq \frac{12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$x < 3$ and $\frac{- 6 x}{- 6} \geq \frac{12}{- 6}$

Divide $x$ by $1$ .

$x < 3$ and $x \geq \frac{12}{- 6}$

Simplify the right side.

Divide $12$ by $- 6$ .

$x < 3$ and $x \geq - 2$

The intersection consists of the elements that are contained in both intervals.

$- 2 \leq x < 3$

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x < 3$

Interval Notation:

$[- 2, 3)$

Solve the System of Inequalities -4x+3>-9 and -6x<=12

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