Pre-Algebra Examples

$- 3 (x - 4) - 5 x < - (3 x + 2) + 2 x$

Step 1

Simplify $- 3 (x - 4) - 5 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 3 x - 3 \cdot - 4 - 5 x < - (3 x + 2) + 2 x$

Step 1.1.2

Multiply $- 3$ by $- 4$ .

$- 3 x + 12 - 5 x < - (3 x + 2) + 2 x$

Step 1.2

Subtract $5 x$ from $- 3 x$ .

$- 8 x + 12 < - (3 x + 2) + 2 x$

Step 2

Simplify $- (3 x + 2) + 2 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 8 x + 12 < - (3 x) - 1 \cdot 2 + 2 x$

Step 2.1.2

Multiply $3$ by $- 1$ .

$- 8 x + 12 < - 3 x - 1 \cdot 2 + 2 x$

Step 2.1.3

Multiply $- 1$ by $2$ .

$- 8 x + 12 < - 3 x - 2 + 2 x$

Step 2.2

Add $- 3 x$ and $2 x$ .

$- 8 x + 12 < - x - 2$

Step 3

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

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Step 3.1

Add $x$ to both sides of the inequality.

$- 8 x + 12 + x < - 2$

Step 3.2

Add $- 8 x$ and $x$ .

$- 7 x + 12 < - 2$

Step 4

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

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Step 4.1

Subtract $12$ from both sides of the inequality.

$- 7 x < - 2 - 12$

Step 4.2

Subtract $12$ from $- 2$ .

$- 7 x < - 14$

Step 5

Divide each term in $- 7 x < - 14$ by $- 7$ and simplify.

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Step 5.1

Divide each term in $- 7 x < - 14$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} > \frac{- 14}{- 7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} > \frac{- 14}{- 7}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 14}{- 7}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 14$ by $- 7$ .

$x > 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$