Pre-Algebra Examples

$- 6 (5 x + 7) < - 36 - 6$

Step 1

Subtract $6$ from $- 36$ .

$- 6 (5 x + 7) < - 42$

Step 2

Divide each term in $- 6 (5 x + 7) < - 42$ by $- 6$ and simplify.

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Step 2.1

Divide each term in $- 6 (5 x + 7) < - 42$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 (5 x + 7)}{- 6} > \frac{- 42}{- 6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 6 (5 x + 7)}{- 6} > \frac{- 42}{- 6}$

Step 2.2.1.2

Divide $5 x + 7$ by $1$ .

$5 x + 7 > \frac{- 42}{- 6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 42$ by $- 6$ .

$5 x + 7 > 7$

Step 3

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

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Step 3.1

Subtract $7$ from both sides of the inequality.

$5 x > 7 - 7$

Step 3.2

Subtract $7$ from $7$ .

$5 x > 0$

Step 4

Divide each term in $5 x > 0$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x > 0$ by $5$ .

$\frac{5 x}{5} > \frac{0}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} > \frac{0}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{0}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $5$ .

$x > 0$

Step 5