Solve the System of Inequalities 6x-4<-34 or 3x+10>10

$6 x - 4 < - 34$ or $3 x + 10 > 10$

Step 1

Simplify the first inequality.

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

Add $4$ to both sides of the inequality.

$6 x < - 34 + 4$ or $3 x + 10 > 10$

Add $- 34$ and $4$ .

$6 x < - 30$ or $3 x + 10 > 10$

Divide each term in $6 x < - 30$ by $6$ and simplify.

Divide each term in $6 x < - 30$ by $6$ .

$\frac{6 x}{6} < \frac{- 30}{6}$ or $3 x + 10 > 10$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} < \frac{- 30}{6}$ or $3 x + 10 > 10$

Divide $x$ by $1$ .

$x < \frac{- 30}{6}$ or $3 x + 10 > 10$

Simplify the right side.

Divide $- 30$ by $6$ .

$x < - 5$ or $3 x + 10 > 10$

Step 2

Simplify the second inequality.

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

Subtract $10$ from both sides of the inequality.

$x < - 5$ or $3 x > 10 - 10$

Subtract $10$ from $10$ .

$x < - 5$ or $3 x > 0$

Divide each term in $3 x > 0$ by $3$ and simplify.

Divide each term in $3 x > 0$ by $3$ .

$x < - 5$ or $\frac{3 x}{3} > \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x < - 5$ or $\frac{3 x}{3} > \frac{0}{3}$

Divide $x$ by $1$ .

$x < - 5$ or $x > \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x < - 5$ or $x > 0$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 5 or x > 0$

Interval Notation:

$(- \infty, - 5) \cup (0, \infty)$

Step 4

Solve the System of Inequalities 6x-4<-34 or 3x+10>10

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