Algebra Examples

$- \frac{3}{4} (4 x + 12) \leq - (2 x + 8)$

Step 1

Simplify $- \frac{3}{4} \cdot (4 x + 12)$ .

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Step 1.1

Rewrite.

$0 + 0 - \frac{3}{4} \cdot (4 x + 12) \leq - (2 x + 8)$

Step 1.2

Simplify by adding zeros.

$- \frac{3}{4} \cdot (4 x + 12) \leq - (2 x + 8)$

Step 1.3

Apply the distributive property.

$- \frac{3}{4} (4 x) - \frac{3}{4} \cdot 12 \leq - (2 x + 8)$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (4 x) - \frac{3}{4} \cdot 12 \leq - (2 x + 8)$

Step 1.4.2

Factor $4$ out of $4 x$ .

$\frac{- 3}{4} (4 (x)) - \frac{3}{4} \cdot 12 \leq - (2 x + 8)$

Step 1.4.3

Cancel the common factor.

$\frac{- 3}{4} (4 x) - \frac{3}{4} \cdot 12 \leq - (2 x + 8)$

Step 1.4.4

Rewrite the expression.

$- 3 x - \frac{3}{4} \cdot 12 \leq - (2 x + 8)$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$- 3 x + \frac{- 3}{4} \cdot 12 \leq - (2 x + 8)$

Step 1.5.2

Factor $4$ out of $12$ .

$- 3 x + \frac{- 3}{4} \cdot (4 (3)) \leq - (2 x + 8)$

Step 1.5.3

Cancel the common factor.

$- 3 x + \frac{- 3}{4} \cdot (4 \cdot 3) \leq - (2 x + 8)$

Step 1.5.4

Rewrite the expression.

$- 3 x - 3 \cdot 3 \leq - (2 x + 8)$

Step 1.6

Multiply $- 3$ by $3$ .

$- 3 x - 9 \leq - (2 x + 8)$

Step 2

Simplify $- (2 x + 8)$ .

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Step 2.1

Apply the distributive property.

$- 3 x - 9 \leq - (2 x) - 1 \cdot 8$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $2$ by $- 1$ .

$- 3 x - 9 \leq - 2 x - 1 \cdot 8$

Step 2.2.2

Multiply $- 1$ by $8$ .

$- 3 x - 9 \leq - 2 x - 8$

Step 3

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

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Step 3.1

Add $2 x$ to both sides of the inequality.

$- 3 x - 9 + 2 x \leq - 8$

Step 3.2

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

$- x - 9 \leq - 8$

Step 4

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

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Step 4.1

Add $9$ to both sides of the inequality.

$- x \leq - 8 + 9$

Step 4.2

Add $- 8$ and $9$ .

$- x \leq 1$

Step 5

Divide each term in $- x \leq 1$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- x \leq 1$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{1}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{1}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x \geq \frac{1}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $1$ by $- 1$ .

$x \geq - 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 1$

Interval Notation:

$[- 1, \infty)$