Solve the Inequality for x -3/4x+2>11

$- \frac{3}{4} x + 2 > 11$

Step 1

Simplify each term.

Combine $x$ and $\frac{3}{4}$ .

$- \frac{x \cdot 3}{4} + 2 > 11$

Move $3$ to the left of $x$ .

$- \frac{3 x}{4} + 2 > 11$

Step 2

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

Subtract $2$ from both sides of the inequality.

$- \frac{3 x}{4} > 11 - 2$

Subtract $2$ from $11$ .

$- \frac{3 x}{4} > 9$

Step 3

Divide each term in $- \frac{3 x}{4} > 9$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x}{4} > 9$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x}{4}}{- 1} < \frac{9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 x}{4}}{1} < \frac{9}{- 1}$

Divide $\frac{3 x}{4}$ by $1$ .

$\frac{3 x}{4} < \frac{9}{- 1}$

Simplify the right side.

Divide $9$ by $- 1$ .

$\frac{3 x}{4} < - 9$

Step 4

Multiply both sides by $4$ .

$\frac{3 x}{4} \cdot 4 < - 9 \cdot 4$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 x}{4} \cdot 4 < - 9 \cdot 4$

Rewrite the expression.

$3 x < - 9 \cdot 4$

Simplify the right side.

Multiply $- 9$ by $4$ .

$3 x < - 36$

Step 6

Divide each term in $3 x < - 36$ by $3$ and simplify.

Divide each term in $3 x < - 36$ by $3$ .

$\frac{3 x}{3} < \frac{- 36}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{- 36}{3}$

Divide $x$ by $1$ .

$x < \frac{- 36}{3}$

Simplify the right side.

Divide $- 36$ by $3$ .

$x < - 12$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x < - 12$

Interval Notation:

$(- \infty, - 12)$

Solve the Inequality for x -3/4x+2>11

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