Algebra Examples

$- \frac{1}{4} (12 x + 8) \leq - 2 x + 11$

Step 1

Simplify $- \frac{1}{4} \cdot (12 x + 8)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 - \frac{1}{4} \cdot (12 x + 8) \leq - 2 x + 11$

Step 1.2

Simplify by adding zeros.

$- \frac{1}{4} \cdot (12 x + 8) \leq - 2 x + 11$

Step 1.3

Apply the distributive property.

$- \frac{1}{4} (12 x) - \frac{1}{4} \cdot 8 \leq - 2 x + 11$

Step 1.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.4.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} (12 x) - \frac{1}{4} \cdot 8 \leq - 2 x + 11$

Step 1.4.2

Factor $4$ out of $12 x$ .

$\frac{- 1}{4} (4 (3 x)) - \frac{1}{4} \cdot 8 \leq - 2 x + 11$

Step 1.4.3

Cancel the common factor.

$\frac{- 1}{4} (4 (3 x)) - \frac{1}{4} \cdot 8 \leq - 2 x + 11$

Step 1.4.4

Rewrite the expression.

$- 1 (3 x) - \frac{1}{4} \cdot 8 \leq - 2 x + 11$

Step 1.5

Multiply $3$ by $- 1$ .

$- 3 x - \frac{1}{4} \cdot 8 \leq - 2 x + 11$

Step 1.6

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.6.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$- 3 x + \frac{- 1}{4} \cdot 8 \leq - 2 x + 11$

Step 1.6.2

Factor $4$ out of $8$ .

$- 3 x + \frac{- 1}{4} \cdot (4 (2)) \leq - 2 x + 11$

Step 1.6.3

Cancel the common factor.

$- 3 x + \frac{- 1}{4} \cdot (4 \cdot 2) \leq - 2 x + 11$

Step 1.6.4

Rewrite the expression.

$- 3 x - 1 \cdot 2 \leq - 2 x + 11$

Step 1.7

Multiply $- 1$ by $2$ .

$- 3 x - 2 \leq - 2 x + 11$

Step 2

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

Tap for more steps...

Step 2.1

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

$- 3 x - 2 + 2 x \leq 11$

Step 2.2

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

$- x - 2 \leq 11$

Step 3

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

Tap for more steps...

Step 3.1

Add $2$ to both sides of the inequality.

$- x \leq 11 + 2$

Step 3.2

Add $11$ and $2$ .

$- x \leq 13$

Step 4

Divide each term in $- x \leq 13$ by $- 1$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $- x \leq 13$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{13}{- 1}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{13}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x \geq \frac{13}{- 1}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $13$ by $- 1$ .

$x \geq - 13$

Step 5