Finite Math Examples

$81.3 < 90 - 5.8 x < 78.4$

Step 1

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

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Step 1.1

Subtract $90$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$81.3 - 90 < - 5.8 x < 78.4 - 90$

Step 1.2

Subtract $90$ from $81.3$ .

$- 8.7 < - 5.8 x < 78.4 - 90$

Step 1.3

Subtract $90$ from $78.4$ .

$- 8.7 < - 5.8 x < - 11.6$

Step 2

Divide each term in the inequality by $- 5.8$ .

$\frac{- 8.7}{- 5.8} > \frac{- 5.8 x}{- 5.8} > \frac{- 11.6}{- 5.8}$

Step 3

Divide $- 8.7$ by $- 5.8$ .

$1.5 > \frac{- 5.8 x}{- 5.8} > \frac{- 11.6}{- 5.8}$

Step 4

Cancel the common factor of $- 5.8$ .

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Step 4.1

Cancel the common factor.

$1.5 > \frac{- 5.8 x}{- 5.8} > \frac{- 11.6}{- 5.8}$

Step 4.2

Divide $x$ by $1$ .

$1.5 > x > \frac{- 11.6}{- 5.8}$

Step 5

Divide $- 11.6$ by $- 5.8$ .

$1.5 > x > 2$

Step 6

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

False