Algebra Examples

$4 x + 2 > 14 - 21 x + 1 > 22$

Step 1

Add $14$ and $1$ .

$4 x + 2 > - 21 x + 15 > 22$

Step 2

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

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Step 2.1

Subtract $15$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$4 x + 2 - 15 > - 21 x > 22 - 15$

Step 2.2

Subtract $15$ from $2$ .

$4 x - 13 > - 21 x > 22 - 15$

Step 2.3

Subtract $15$ from $22$ .

$4 x - 13 > - 21 x > 7$

Step 3

Divide each term in the inequality by $- 21$ .

$\frac{4 x}{- 21} + \frac{- 13}{- 21} < \frac{- 21 x}{- 21} < \frac{7}{- 21}$

Step 4

Simplify each term.

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Step 4.1

Move the negative in front of the fraction.

$- \frac{4 x}{21} + \frac{- 13}{- 21} < \frac{- 21 x}{- 21} < \frac{7}{- 21}$

Step 4.2

Dividing two negative values results in a positive value.

$- \frac{4 x}{21} + \frac{13}{21} < \frac{- 21 x}{- 21} < \frac{7}{- 21}$

Step 5

Cancel the common factor of $- 21$ .

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Step 5.1

Cancel the common factor.

$- \frac{4 x}{21} + \frac{13}{21} < \frac{- 21 x}{- 21} < \frac{7}{- 21}$

Step 5.2

Divide $x$ by $1$ .

$- \frac{4 x}{21} + \frac{13}{21} < x < \frac{7}{- 21}$

Step 6

Cancel the common factor of $7$ and $- 21$ .

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Step 6.1

Factor $7$ out of $7$ .

$- \frac{4 x}{21} + \frac{13}{21} < x < \frac{7 (1)}{- 21}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $7$ out of $- 21$ .

$- \frac{4 x}{21} + \frac{13}{21} < x < \frac{7 \cdot 1}{7 \cdot - 3}$

Step 6.2.2

Cancel the common factor.

$- \frac{4 x}{21} + \frac{13}{21} < x < \frac{7 \cdot 1}{7 \cdot - 3}$

Step 6.2.3

Rewrite the expression.

$- \frac{4 x}{21} + \frac{13}{21} < x < \frac{1}{- 3}$

Step 7

Move the negative in front of the fraction.

$- \frac{4 x}{21} + \frac{13}{21} < x < - \frac{1}{3}$

Step 8