Solve for x -7>3x+2>7

$- 7 > 3 x + 2 > 7$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 7 - 2 > 3 x > 7 - 2$

Subtract $2$ from $- 7$ .

$- 9 > 3 x > 7 - 2$

Subtract $2$ from $7$ .

$- 9 > 3 x > 5$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 9}{3} > \frac{3 x}{3} > \frac{5}{3}$

Step 3

Divide $- 9$ by $3$ .

$- 3 > \frac{3 x}{3} > \frac{5}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 3 > \frac{3 x}{3} > \frac{5}{3}$

Divide $x$ by $1$ .

$- 3 > x > \frac{5}{3}$

Step 5

Since the inequality can never be true, there is no solution.

False