Solve the Inequality for x 6x-13<6(x-2)

$6 x - 13 < 6 (x - 2)$

Simplify $6 (x - 2)$ .

Rewrite.

$6 x - 13 < 0 + 0 + 6 (x - 2)$

Simplify by adding zeros.

$6 x - 13 < 6 (x - 2)$

Apply the distributive property.

$6 x - 13 < 6 x + 6 \cdot - 2$

Multiply $6$ by $- 2$ .

$6 x - 13 < 6 x - 12$

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

Subtract $6 x$ from both sides of the inequality.

$6 x - 13 - 6 x < - 12$

Combine the opposite terms in $6 x - 13 - 6 x$ .

Subtract $6 x$ from $6 x$ .

$0 - 13 < - 12$

Subtract $13$ from $0$ .

$- 13 < - 12$

Since $- 13 < - 12$ , the inequality will always be true.

Always true

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$