Evaluate 2(-3x+1)<14

$2 (- 3 x + 1) < 14$

Step 1

Divide each term in $2 (- 3 x + 1) < 14$ by $2$ and simplify.

Divide each term in $2 (- 3 x + 1) < 14$ by $2$ .

$\frac{2 (- 3 x + 1)}{2} < \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (- 3 x + 1)}{2} < \frac{14}{2}$

Divide $- 3 x + 1$ by $1$ .

$- 3 x + 1 < \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$- 3 x + 1 < 7$

Step 2

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

Subtract $1$ from both sides of the inequality.

$- 3 x < 7 - 1$

Subtract $1$ from $7$ .

$- 3 x < 6$

Step 3

Divide each term in $- 3 x < 6$ by $- 3$ and simplify.

Divide each term in $- 3 x < 6$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{6}{- 3}$

Divide $x$ by $1$ .

$x > \frac{6}{- 3}$

Simplify the right side.

Divide $6$ by $- 3$ .

$x > - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - 2$

Interval Notation:

$(- 2, \infty)$

Evaluate 2(-3x+1)<14

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