Pre-Algebra Examples

$- x - 5 > 3 x + 7$

Step 1

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

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Step 1.1

Subtract $3 x$ from both sides of the inequality.

$- x - 5 - 3 x > 7$

Step 1.2

Subtract $3 x$ from $- x$ .

$- 4 x - 5 > 7$

Step 2

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

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Step 2.1

Add $5$ to both sides of the inequality.

$- 4 x > 7 + 5$

Step 2.2

Add $7$ and $5$ .

$- 4 x > 12$

Step 3

Divide each term in $- 4 x > 12$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 x > 12$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{12}{- 4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{12}{- 4}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{12}{- 4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $12$ by $- 4$ .

$x < - 3$

Step 4