Solve the System of Inequalities 2x-2<4 or 3x-1>8

$2 x - 2 < 4$ or $3 x - 1 > 8$

Step 1

Simplify the first inequality.

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

Add $2$ to both sides of the inequality.

$2 x < 4 + 2$ or $3 x - 1 > 8$

Add $4$ and $2$ .

$2 x < 6$ or $3 x - 1 > 8$

Divide each term in $2 x < 6$ by $2$ and simplify.

Divide each term in $2 x < 6$ by $2$ .

$\frac{2 x}{2} < \frac{6}{2}$ or $3 x - 1 > 8$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{6}{2}$ or $3 x - 1 > 8$

Divide $x$ by $1$ .

$x < \frac{6}{2}$ or $3 x - 1 > 8$

Simplify the right side.

Divide $6$ by $2$ .

$x < 3$ or $3 x - 1 > 8$

Step 2

Simplify the second inequality.

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

Add $1$ to both sides of the inequality.

$x < 3$ or $3 x > 8 + 1$

Add $8$ and $1$ .

$x < 3$ or $3 x > 9$

Divide each term in $3 x > 9$ by $3$ and simplify.

Divide each term in $3 x > 9$ by $3$ .

$x < 3$ or $\frac{3 x}{3} > \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x < 3$ or $\frac{3 x}{3} > \frac{9}{3}$

Divide $x$ by $1$ .

$x < 3$ or $x > \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x < 3$ or $x > 3$

Step 3

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

$x \neq 3$

Step 4

The result can be shown in multiple forms.

$x \neq 3$

Interval Notation:

$(- \infty, 3) \cup (3, \infty)$

Step 5

Solve the System of Inequalities 2x-2<4 or 3x-1>8

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