Pre-Algebra Examples

$10 x - 19 < 9 - 4 x < 4 x + 25$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $9$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$10 x - 19 - 9 < - 4 x < 4 x + 25 - 9$

Step 1.2

Subtract $9$ from $- 19$ .

$10 x - 28 < - 4 x < 4 x + 25 - 9$

Step 1.3

Subtract $9$ from $25$ .

$10 x - 28 < - 4 x < 4 x + 16$

Step 2

Divide each term in the inequality by $- 4$ .

$\frac{10 x}{- 4} + \frac{- 28}{- 4} > \frac{- 4 x}{- 4} > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Cancel the common factor of $10$ and $- 4$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $10 x$ .

$\frac{2 (5 x)}{- 4} + \frac{- 28}{- 4} > \frac{- 4 x}{- 4} > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Factor $2$ out of $- 4$ .

$\frac{2 (5 x)}{2 (- 2)} + \frac{- 28}{- 4} > \frac{- 4 x}{- 4} > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 3.1.2.2

Cancel the common factor.

$\frac{2 (5 x)}{2 \cdot - 2} + \frac{- 28}{- 4} > \frac{- 4 x}{- 4} > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 3.1.2.3

Rewrite the expression.

$\frac{5 x}{- 2} + \frac{- 28}{- 4} > \frac{- 4 x}{- 4} > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{5 x}{2} + \frac{- 28}{- 4} > \frac{- 4 x}{- 4} > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 3.3

Divide $- 28$ by $- 4$ .

$- \frac{5 x}{2} + 7 > \frac{- 4 x}{- 4} > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 4

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

$- \frac{5 x}{2} + 7 > \frac{- 4 x}{- 4} > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 4.2

Divide $x$ by $1$ .

$- \frac{5 x}{2} + 7 > x > \frac{4 x}{- 4} + \frac{16}{- 4}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Cancel the common factor of $4$ and $- 4$ .

Tap for more steps...

Step 5.1.1

Factor $4$ out of $4 x$ .

$- \frac{5 x}{2} + 7 > x > \frac{4 (x)}{- 4} + \frac{16}{- 4}$

Step 5.1.2

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$- \frac{5 x}{2} + 7 > x > - 1 \cdot x + \frac{16}{- 4}$

Step 5.2

Rewrite $- 1 \cdot x$ as $- x$ .

$- \frac{5 x}{2} + 7 > x > - x + \frac{16}{- 4}$

Step 5.3

Divide $16$ by $- 4$ .

$- \frac{5 x}{2} + 7 > x > - x - 4$

Step 6