Pre-Algebra Examples

$52 < 4 - 3 x < 13$

Step 1

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

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Step 1.1

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

$52 - 4 < - 3 x < 13 - 4$

Step 1.2

Subtract $4$ from $52$ .

$48 < - 3 x < 13 - 4$

Step 1.3

Subtract $4$ from $13$ .

$48 < - 3 x < 9$

Step 2

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

$\frac{48}{- 3} > \frac{- 3 x}{- 3} > \frac{9}{- 3}$

Step 3

Divide $48$ by $- 3$ .

$- 16 > \frac{- 3 x}{- 3} > \frac{9}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

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Step 4.1

Cancel the common factor.

$- 16 > \frac{- 3 x}{- 3} > \frac{9}{- 3}$

Step 4.2

Divide $x$ by $1$ .

$- 16 > x > \frac{9}{- 3}$

Step 5

Divide $9$ by $- 3$ .

$- 16 > x > - 3$

Step 6

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

False

Step 7