Solve the Inequality for x (x-13)/-6<3

$\frac{x - 13}{- 6} < 3$

Step 1

Multiply both sides by $- 6$ .

$\frac{x - 13}{- 6} \cdot - 6 > 3 \cdot - 6$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{x - 13}{- 6} \cdot - 6$ .

Simplify terms.

Cancel the common factor of $6$ .

Factor $6$ out of $- 6$ .

$\frac{x - 13}{6 (- 1)} \cdot - 6 > 3 \cdot - 6$

Factor $6$ out of $- 6$ .

$\frac{x - 13}{6 \cdot - 1} \cdot (6 \cdot - 1) > 3 \cdot - 6$

Cancel the common factor.

$\frac{x - 13}{6 \cdot - 1} \cdot (6 \cdot - 1) > 3 \cdot - 6$

Rewrite the expression.

$\frac{x - 13}{- 1} \cdot - 1 > 3 \cdot - 6$

Combine $\frac{x - 13}{- 1}$ and $- 1$ .

$\frac{(x - 13) \cdot - 1}{- 1} > 3 \cdot - 6$

Simplify the expression.

Move the negative one from the denominator of $\frac{(x - 13) \cdot - 1}{- 1}$ .

$- 1 \cdot ((x - 13) \cdot - 1) > 3 \cdot - 6$

Rewrite $- 1 \cdot ((x - 13) \cdot - 1)$ as $- ((x - 13) \cdot - 1)$ .

$- ((x - 13) \cdot - 1) > 3 \cdot - 6$

Apply the distributive property.

$- (x \cdot - 1 - 13 \cdot - 1) > 3 \cdot - 6$

Simplify the expression.

Move $- 1$ to the left of $x$ .

$- (- 1 \cdot x - 13 \cdot - 1) > 3 \cdot - 6$

Multiply $- 13$ by $- 1$ .

$- (- 1 \cdot x + 13) > 3 \cdot - 6$

Rewrite $- 1 x$ as $- x$ .

$- (- x + 13) > 3 \cdot - 6$

Apply the distributive property.

$- - x - 1 \cdot 13 > 3 \cdot - 6$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$1 x - 1 \cdot 13 > 3 \cdot - 6$

Multiply $x$ by $1$ .

$x - 1 \cdot 13 > 3 \cdot - 6$

Multiply $- 1$ by $13$ .

$x - 13 > 3 \cdot - 6$

Simplify the right side.

Multiply $3$ by $- 6$ .

$x - 13 > - 18$

Step 3

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

Add $13$ to both sides of the inequality.

$x > - 18 + 13$

Add $- 18$ and $13$ .

$x > - 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - 5$

Interval Notation:

$(- 5, \infty)$

Solve the Inequality for x (x-13)/-6<3

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