Solve the System of Inequalities 5>=5x-5 or 5x-5>=20

$5 \geq 5 x - 5$ or $5 x - 5 \geq 20$

Step 1

Simplify the first inequality.

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

$5 x - 5 \leq 5$

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

Add $5$ to both sides of the inequality.

$5 x \leq 5 + 5$

Add $5$ and $5$ .

$5 x \leq 10$

Divide each term in $5 x \leq 10$ by $5$ and simplify.

Divide each term in $5 x \leq 10$ by $5$ .

$\frac{5 x}{5} \leq \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \leq \frac{10}{5}$

Divide $x$ by $1$ .

$x \leq \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$x \leq 2$

Step 2

Simplify the second inequality.

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

Add $5$ to both sides of the inequality.

$5 x \geq 20 + 5$

Add $20$ and $5$ .

$5 x \geq 25$

Divide each term in $5 x \geq 25$ by $5$ and simplify.

Divide each term in $5 x \geq 25$ by $5$ .

$\frac{5 x}{5} \geq \frac{25}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{25}{5}$

Divide $x$ by $1$ .

$x \geq \frac{25}{5}$

Simplify the right side.

Divide $25$ by $5$ .

$x \geq 5$

Step 3

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

$x \leq 2$ or $x \geq 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 2 or x \geq 5$

Interval Notation:

$(- \infty, 2] \cup [5, \infty)$

Step 5

Solve the System of Inequalities 5>=5x-5 or 5x-5>=20

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