Algebra Examples

$18 x - 9 > 92 x - 4 > - 10$

Step 1

Solve $18 x - 9 > 92 x - 4$ for $x$ .

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Step 1.1

Move all terms containing $x$ to the left side of the inequality.

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Step 1.1.1

Subtract $92 x$ from both sides of the inequality.

$18 x - 9 - 92 x > - 4$

Step 1.1.2

Subtract $92 x$ from $18 x$ .

$- 74 x - 9 > - 4$

Step 1.2

Move all terms not containing $x$ to the right side of the inequality.

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Step 1.2.1

Add $9$ to both sides of the inequality.

$- 74 x > - 4 + 9$

Step 1.2.2

Add $- 4$ and $9$ .

$- 74 x > 5$

Step 1.3

Divide each term in $- 74 x > 5$ by $- 74$ and simplify.

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Step 1.3.1

Divide each term in $- 74 x > 5$ by $- 74$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 74 x}{- 74} < \frac{5}{- 74}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 74$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 74 x}{- 74} < \frac{5}{- 74}$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x < \frac{5}{- 74}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$x < - \frac{5}{74}$

Step 2

Solve $92 x - 4 > - 10$ for $x$ .

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Step 2.1

Move all terms not containing $x$ to the right side of the inequality.

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Step 2.1.1

Add $4$ to both sides of the inequality.

$92 x > - 10 + 4$

Step 2.1.2

Add $- 10$ and $4$ .

$92 x > - 6$

Step 2.2

Divide each term in $92 x > - 6$ by $92$ and simplify.

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Step 2.2.1

Divide each term in $92 x > - 6$ by $92$ .

$\frac{92 x}{92} > \frac{- 6}{92}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $92$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{92 x}{92} > \frac{- 6}{92}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 6}{92}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Cancel the common factor of $- 6$ and $92$ .

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Step 2.2.3.1.1

Factor $2$ out of $- 6$ .

$x > \frac{2 (- 3)}{92}$

Step 2.2.3.1.2

Cancel the common factors.

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Step 2.2.3.1.2.1

Factor $2$ out of $92$ .

$x > \frac{2 \cdot - 3}{2 \cdot 46}$

Step 2.2.3.1.2.2

Cancel the common factor.

$x > \frac{2 \cdot - 3}{2 \cdot 46}$

Step 2.2.3.1.2.3

Rewrite the expression.

$x > \frac{- 3}{46}$

Step 2.2.3.2

Move the negative in front of the fraction.

$x > - \frac{3}{46}$

Step 3

Find the intersection of $x < - \frac{5}{74}$ and $x > - \frac{3}{46}$ .

No solution