Solve the System of Inequalities 4x-6<10 or 30<4x-6

$4 x - 6 < 10$ or $30 < 4 x - 6$

Simplify the first inequality.

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

Add $6$ to both sides of the inequality.

$4 x < 10 + 6$ or $30 < 4 x - 6$

Add $10$ and $6$ .

$4 x < 16$ or $30 < 4 x - 6$

Divide each term in $4 x < 16$ by $4$ and simplify.

Divide each term in $4 x < 16$ by $4$ .

$\frac{4 x}{4} < \frac{16}{4}$ or $30 < 4 x - 6$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} < \frac{16}{4}$ or $30 < 4 x - 6$

Divide $x$ by $1$ .

$x < \frac{16}{4}$ or $30 < 4 x - 6$

Simplify the right side.

Divide $16$ by $4$ .

$x < 4$ or $30 < 4 x - 6$

Simplify the second inequality.

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

$x < 4$ or $4 x - 6 > 30$

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

Add $6$ to both sides of the inequality.

$x < 4$ or $4 x > 30 + 6$

Add $30$ and $6$ .

$x < 4$ or $4 x > 36$

Divide each term in $4 x > 36$ by $4$ and simplify.

Divide each term in $4 x > 36$ by $4$ .

$x < 4$ or $\frac{4 x}{4} > \frac{36}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$x < 4$ or $\frac{4 x}{4} > \frac{36}{4}$

Divide $x$ by $1$ .

$x < 4$ or $x > \frac{36}{4}$

Simplify the right side.

Divide $36$ by $4$ .

$x < 4$ or $x > 9$

The result can be shown in multiple forms.

Inequality Form:

$x < 4 or x > 9$

Interval Notation:

$(- \infty, 4) \cup (9, \infty)$