Calculus Examples

$2 x - 4 > 8 x + 2$

Step 1

Move all terms containing $x$ to the left side of the inequality.

Tap for more steps...

Step 1.1

Subtract $8 x$ from both sides of the inequality.

$2 x - 4 - 8 x > 2$

Step 1.2

Subtract $8 x$ from $2 x$ .

$- 6 x - 4 > 2$

Step 2

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

Tap for more steps...

Step 2.1

Add $4$ to both sides of the inequality.

$- 6 x > 2 + 4$

Step 2.2

Add $2$ and $4$ .

$- 6 x > 6$

Step 3

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

Tap for more steps...

Step 3.1

Divide each term in $- 6 x > 6$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 x}{- 6} < \frac{6}{- 6}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $- 6$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} < \frac{6}{- 6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{6}{- 6}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $6$ by $- 6$ .

$x < - 1$

Step 4

Convert the inequality to interval notation.

$(- \infty, - 1)$

Step 5