Solve the System of Inequalities 9-4x>=5 or 4(-1+x)-6>=2

$9 - 4 x \geq 5$ or $4 (- 1 + x) - 6 \geq 2$

Simplify the first inequality.

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

Subtract $9$ from both sides of the inequality.

$- 4 x \geq 5 - 9$

Subtract $9$ from $5$ .

$- 4 x \geq - 4$

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

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

$\frac{- 4 x}{- 4} \leq \frac{- 4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \leq \frac{- 4}{- 4}$

Divide $x$ by $1$ .

$x \leq \frac{- 4}{- 4}$

Simplify the right side.

Divide $- 4$ by $- 4$ .

$x \leq 1$

Simplify the second inequality.

Simplify $4 (- 1 + x) - 6$ .

Simplify each term.

Apply the distributive property.

$4 \cdot - 1 + 4 x - 6 \geq 2$

Multiply $4$ by $- 1$ .

$- 4 + 4 x - 6 \geq 2$

Subtract $6$ from $- 4$ .

$4 x - 10 \geq 2$

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

Add $10$ to both sides of the inequality.

$4 x \geq 2 + 10$

Add $2$ and $10$ .

$4 x \geq 12$

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

Divide each term in $4 x \geq 12$ by $4$ .

$\frac{4 x}{4} \geq \frac{12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{12}{4}$

Divide $x$ by $1$ .

$x \geq \frac{12}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$x \geq 3$

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

$x \leq 1$ or $x \geq 3$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 1 or x \geq 3$

Interval Notation:

$(- \infty, 1] \cup [3, \infty)$

Solve the System of Inequalities 9-4x>=5 or 4(-1+x)-6>=2

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