Graph -1/4(12x+8)<=-2x+11

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

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

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $12 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $- 1$ .

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

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $2$ .

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

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

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

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

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

$- x - 2 \leq 11$

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

Add $2$ to both sides of the inequality.

$- x \leq 11 + 2$

Add $11$ and $2$ .

$- x \leq 13$

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

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.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $13$ by $- 1$ .

$x \geq - 13$

Graph -1/4(12x+8)<=-2x+11

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