Solve the Inequality for x -x<-x+7(x-2)

$- x < - x + 7 (x - 2)$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$- x + 7 (x - 2) > - x$

Step 2

Simplify $- x + 7 (x - 2)$ .

Simplify each term.

Apply the distributive property.

$- x + 7 x + 7 \cdot - 2 > - x$

Multiply $7$ by $- 2$ .

$- x + 7 x - 14 > - x$

Add $- x$ and $7 x$ .

$6 x - 14 > - x$

Step 3

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

Add $x$ to both sides of the inequality.

$6 x - 14 + x > 0$

Add $6 x$ and $x$ .

$7 x - 14 > 0$

Step 4

Add $14$ to both sides of the inequality.

$7 x > 14$

Step 5

Divide each term in $7 x > 14$ by $7$ and simplify.

Divide each term in $7 x > 14$ by $7$ .

$\frac{7 x}{7} > \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} > \frac{14}{7}$

Divide $x$ by $1$ .

$x > \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$x > 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$