Solve for x -3>=-3x+4>10

$- 3 \geq - 3 x + 4 > 10$

Step 1

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

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 - 4 \geq - 3 x > 10 - 4$

Subtract $4$ from $- 3$ .

$- 7 \geq - 3 x > 10 - 4$

Subtract $4$ from $10$ .

$- 7 \geq - 3 x > 6$

Step 2

Divide each term in the inequality by $- 3$ .

$\frac{- 7}{- 3} \leq \frac{- 3 x}{- 3} < \frac{6}{- 3}$

Step 3

Dividing two negative values results in a positive value.

$\frac{7}{3} \leq \frac{- 3 x}{- 3} < \frac{6}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{7}{3} \leq \frac{- 3 x}{- 3} < \frac{6}{- 3}$

Divide $x$ by $1$ .

$\frac{7}{3} \leq x < \frac{6}{- 3}$

Step 5

Divide $6$ by $- 3$ .

$\frac{7}{3} \leq x < - 2$

Step 6

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

False