Algebra Examples

$4 x - 18 > 2 - 17 x - 8 \leq - 25$

Step 1

Subtract $8$ from $2$ .

$4 x - 18 > - 17 x - 6 \leq - 25$

Step 2

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

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Step 2.1

Add $6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$4 x - 18 + 6 > - 17 x \leq - 25 + 6$

Step 2.2

Add $- 18$ and $6$ .

$4 x - 12 > - 17 x \leq - 25 + 6$

Step 2.3

Add $- 25$ and $6$ .

$4 x - 12 > - 17 x \leq - 19$

Step 3

Divide each term in the inequality by $- 17$ .

$\frac{4 x}{- 17} + \frac{- 12}{- 17} < \frac{- 17 x}{- 17} \geq \frac{- 19}{- 17}$

Step 4

Simplify each term.

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Step 4.1

Move the negative in front of the fraction.

$- \frac{4 x}{17} + \frac{- 12}{- 17} < \frac{- 17 x}{- 17} \geq \frac{- 19}{- 17}$

Step 4.2

Dividing two negative values results in a positive value.

$- \frac{4 x}{17} + \frac{12}{17} < \frac{- 17 x}{- 17} \geq \frac{- 19}{- 17}$

Step 5

Cancel the common factor of $- 17$ .

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Step 5.1

Cancel the common factor.

$- \frac{4 x}{17} + \frac{12}{17} < \frac{- 17 x}{- 17} \geq \frac{- 19}{- 17}$

Step 5.2

Divide $x$ by $1$ .

$- \frac{4 x}{17} + \frac{12}{17} < x \geq \frac{- 19}{- 17}$

Step 6

Dividing two negative values results in a positive value.

$- \frac{4 x}{17} + \frac{12}{17} < x \geq \frac{19}{17}$

Step 7