Solve the Inequality for x 3/4x>-1-(2x-3)

$\frac{3}{4} x > - 1 - (2 x - 3)$

Simplify $\frac{3}{4} x$ .

Rewrite.

$0 + 0 + \frac{3}{4} x > - 1 - (2 x - 3)$

Simplify by adding zeros.

$\frac{3}{4} x > - 1 - (2 x - 3)$

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

$\frac{3 x}{4} > - 1 - (2 x - 3)$

Simplify $- 1 - (2 x - 3)$ .

Simplify each term.

Apply the distributive property.

$\frac{3 x}{4} > - 1 - (2 x) - - 3$

Multiply $2$ by $- 1$ .

$\frac{3 x}{4} > - 1 - 2 x - - 3$

Multiply $- 1$ by $- 3$ .

$\frac{3 x}{4} > - 1 - 2 x + 3$

Add $- 1$ and $3$ .

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

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

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

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

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Combine $2 x$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $3 x + 2 x \cdot 4$ .

Factor $x$ out of $3 x$ .

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

Factor $x$ out of $2 x \cdot 4$ .

$\frac{x \cdot 3 + x (2 \cdot 4)}{4} > 2$

Factor $x$ out of $x \cdot 3 + x (2 \cdot 4)$ .

$\frac{x (3 + 2 \cdot 4)}{4} > 2$

Multiply $2$ by $4$ .

$\frac{x (3 + 8)}{4} > 2$

Add $3$ and $8$ .

$\frac{x \cdot 11}{4} > 2$

Move $11$ to the left of $x$ .

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

Multiply both sides by $4$ .

$\frac{11 x}{4} \cdot 4 > 2 \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{11 x}{4} \cdot 4 > 2 \cdot 4$

Rewrite the expression.

$11 x > 2 \cdot 4$

Simplify the right side.

Multiply $2$ by $4$ .

$11 x > 8$

Divide each term in $11 x > 8$ by $11$ and simplify.

Divide each term in $11 x > 8$ by $11$ .

$\frac{11 x}{11} > \frac{8}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} > \frac{8}{11}$

Divide $x$ by $1$ .

$x > \frac{8}{11}$

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{8}{11}$

Interval Notation:

$(\frac{8}{11}, \infty)$

Solve the Inequality for x 3/4x>-1-(2x-3)

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