Solve the System of Inequalities 5x-5<5 and 5x-5<=20

$5 x - 5 < 5$ and $5 x - 5 \leq 20$

Simplify the first inequality.

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

Add $5$ to both sides of the inequality.

$5 x < 5 + 5$ and $5 x - 5 \leq 20$

Add $5$ and $5$ .

$5 x < 10$ and $5 x - 5 \leq 20$

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

Divide each term in $5 x < 10$ by $5$ .

$\frac{5 x}{5} < \frac{10}{5}$ and $5 x - 5 \leq 20$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} < \frac{10}{5}$ and $5 x - 5 \leq 20$

Divide $x$ by $1$ .

$x < \frac{10}{5}$ and $5 x - 5 \leq 20$

Simplify the right side.

Divide $10$ by $5$ .

$x < 2$ and $5 x - 5 \leq 20$

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.

$x < 2$ and $5 x \leq 20 + 5$

Add $20$ and $5$ .

$x < 2$ and $5 x \leq 25$

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

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

$x < 2$ and $\frac{5 x}{5} \leq \frac{25}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$x < 2$ and $\frac{5 x}{5} \leq \frac{25}{5}$

Divide $x$ by $1$ .

$x < 2$ and $x \leq \frac{25}{5}$

Simplify the right side.

Divide $25$ by $5$ .

$x < 2$ and $x \leq 5$

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

$x < 2$

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$