Solve the System of Inequalities 4x+1<=-11 and -3>4x+1

$4 x + 1 \leq - 11$ and $- 3 > 4 x + 1$

Simplify the first inequality.

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

Subtract $1$ from both sides of the inequality.

$4 x \leq - 11 - 1$ and $- 3 > 4 x + 1$

Subtract $1$ from $- 11$ .

$4 x \leq - 12$ and $- 3 > 4 x + 1$

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

Divide each term in $4 x \leq - 12$ by $4$ .

$\frac{4 x}{4} \leq \frac{- 12}{4}$ and $- 3 > 4 x + 1$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \leq \frac{- 12}{4}$ and $- 3 > 4 x + 1$

Divide $x$ by $1$ .

$x \leq \frac{- 12}{4}$ and $- 3 > 4 x + 1$

Simplify the right side.

Divide $- 12$ by $4$ .

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

Simplify the second inequality.

Rewrite so $x$ is on the left side of the inequality.

$x \leq - 3$ and $4 x + 1 < - 3$

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

Subtract $1$ from both sides of the inequality.

$x \leq - 3$ and $4 x < - 3 - 1$

Subtract $1$ from $- 3$ .

$x \leq - 3$ and $4 x < - 4$

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

Divide each term in $4 x < - 4$ by $4$ .

$x \leq - 3$ and $\frac{4 x}{4} < \frac{- 4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$x \leq - 3$ and $\frac{4 x}{4} < \frac{- 4}{4}$

Divide $x$ by $1$ .

$x \leq - 3$ and $x < \frac{- 4}{4}$

Simplify the right side.

Divide $- 4$ by $4$ .

$x \leq - 3$ and $x < - 1$

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

$x \leq - 3$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 3$

Interval Notation:

$(- \infty, - 3]$

Solve the System of Inequalities 4x+1<=-11 and -3>4x+1

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