Solve the Inequality for x 3/4x+5>11

$\frac{3}{4} x + 5 > 11$

Step 1

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

$\frac{3 x}{4} + 5 > 11$

Step 2

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

Subtract $5$ from both sides of the inequality.

$\frac{3 x}{4} > 11 - 5$

Subtract $5$ from $11$ .

$\frac{3 x}{4} > 6$

Step 3

Multiply both sides by $4$ .

$\frac{3 x}{4} \cdot 4 > 6 \cdot 4$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 x}{4} \cdot 4 > 6 \cdot 4$

Rewrite the expression.

$3 x > 6 \cdot 4$

Simplify the right side.

Multiply $6$ by $4$ .

$3 x > 24$

Step 5

Divide each term in $3 x > 24$ by $3$ and simplify.

Divide each term in $3 x > 24$ by $3$ .

$\frac{3 x}{3} > \frac{24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{24}{3}$

Divide $x$ by $1$ .

$x > \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

$x > 8$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 8$

Interval Notation:

$(8, \infty)$