Algebra Examples

$10 x + 6 y < 30$ , $6 x - 10 y > 30$

Step 1

Simplify the first inequality.

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Step 1.1

Subtract $6 y$ from both sides of the inequality.

$10 x < 30 - 6 y$ and $6 x - 10 y > 30$

Step 1.2

Divide each term in $10 x < 30 - 6 y$ by $10$ and simplify.

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Step 1.2.1

Divide each term in $10 x < 30 - 6 y$ by $10$ .

$\frac{10 x}{10} < \frac{30}{10} + \frac{- 6 y}{10}$ and $6 x - 10 y > 30$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $10$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} < \frac{30}{10} + \frac{- 6 y}{10}$ and $6 x - 10 y > 30$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{30}{10} + \frac{- 6 y}{10}$ and $6 x - 10 y > 30$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $30$ by $10$ .

$x < 3 + \frac{- 6 y}{10}$ and $6 x - 10 y > 30$

Step 1.2.3.1.2

Cancel the common factor of $- 6$ and $10$ .

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Step 1.2.3.1.2.1

Factor $2$ out of $- 6 y$ .

$x < 3 + \frac{2 (- 3 y)}{10}$ and $6 x - 10 y > 30$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $10$ .

$x < 3 + \frac{2 (- 3 y)}{2 (5)}$ and $6 x - 10 y > 30$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x < 3 + \frac{2 (- 3 y)}{2 \cdot 5}$ and $6 x - 10 y > 30$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x < 3 + \frac{- 3 y}{5}$ and $6 x - 10 y > 30$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x < 3 - \frac{3 y}{5}$ and $6 x - 10 y > 30$

Step 2

Simplify the second inequality.

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Step 2.1

Add $10 y$ to both sides of the inequality.

$x < 3 - \frac{3 y}{5}$ and $6 x > 30 + 10 y$

Step 2.2

Divide each term in $6 x > 30 + 10 y$ by $6$ and simplify.

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Step 2.2.1

Divide each term in $6 x > 30 + 10 y$ by $6$ .

$x < 3 - \frac{3 y}{5}$ and $\frac{6 x}{6} > \frac{30}{6} + \frac{10 y}{6}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $6$ .

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Step 2.2.2.1.1

Cancel the common factor.

$x < 3 - \frac{3 y}{5}$ and $\frac{6 x}{6} > \frac{30}{6} + \frac{10 y}{6}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < 3 - \frac{3 y}{5}$ and $x > \frac{30}{6} + \frac{10 y}{6}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Divide $30$ by $6$ .

$x < 3 - \frac{3 y}{5}$ and $x > 5 + \frac{10 y}{6}$

Step 2.2.3.1.2

Cancel the common factor of $10$ and $6$ .

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Step 2.2.3.1.2.1

Factor $2$ out of $10 y$ .

$x < 3 - \frac{3 y}{5}$ and $x > 5 + \frac{2 (5 y)}{6}$

Step 2.2.3.1.2.2

Cancel the common factors.

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Step 2.2.3.1.2.2.1

Factor $2$ out of $6$ .

$x < 3 - \frac{3 y}{5}$ and $x > 5 + \frac{2 (5 y)}{2 (3)}$

Step 2.2.3.1.2.2.2

Cancel the common factor.

$x < 3 - \frac{3 y}{5}$ and $x > 5 + \frac{2 (5 y)}{2 \cdot 3}$

Step 2.2.3.1.2.2.3

Rewrite the expression.

$x < 3 - \frac{3 y}{5}$ and $x > 5 + \frac{5 y}{3}$

Step 3