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

$\frac{x}{4} \geq - 1$ and $- 4 x - 4 \leq - 3$

Step 1

Simplify the first inequality.

Multiply both sides by $4$ .

$\frac{x}{4} \cdot 4 \geq - 1 \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x}{4} \cdot 4 \geq - 1 \cdot 4$

Rewrite the expression.

$x \geq - 1 \cdot 4$

Simplify the right side.

Multiply $- 1$ by $4$ .

$x \geq - 4$

Step 2

Simplify the second inequality.

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

Add $4$ to both sides of the inequality.

$- 4 x \leq - 3 + 4$

Add $- 3$ and $4$ .

$- 4 x \leq 1$

Divide each term in $- 4 x \leq 1$ by $- 4$ and simplify.

Divide each term in $- 4 x \leq 1$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \geq \frac{1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \geq \frac{1}{- 4}$

Divide $x$ by $1$ .

$x \geq \frac{1}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$x \geq - \frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \geq - \frac{1}{4}$

Interval Notation:

$[- \frac{1}{4}, \infty)$

Step 4

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

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