Solve the Inequality for x -1>10x-3(3x+3/2)

$- 1 > 10 x - 3 (3 x + \frac{3}{2})$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$10 x - 3 (3 x + \frac{3}{2}) < - 1$

Step 2

Simplify $10 x - 3 (3 x + \frac{3}{2})$ .

Simplify each term.

Apply the distributive property.

$10 x - 3 (3 x) - 3 (\frac{3}{2}) < - 1$

Multiply $3$ by $- 3$ .

$10 x - 9 x - 3 (\frac{3}{2}) < - 1$

Multiply $- 3 (\frac{3}{2})$ .

Combine $- 3$ and $\frac{3}{2}$ .

$10 x - 9 x + \frac{- 3 \cdot 3}{2} < - 1$

Multiply $- 3$ by $3$ .

$10 x - 9 x + \frac{- 9}{2} < - 1$

Move the negative in front of the fraction.

$10 x - 9 x - \frac{9}{2} < - 1$

Subtract $9 x$ from $10 x$ .

$x - \frac{9}{2} < - 1$

Step 3

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

Add $\frac{9}{2}$ to both sides of the inequality.

$x < - 1 + \frac{9}{2}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x < - 1 \cdot \frac{2}{2} + \frac{9}{2}$

Combine $- 1$ and $\frac{2}{2}$ .

$x < \frac{- 1 \cdot 2}{2} + \frac{9}{2}$

Combine the numerators over the common denominator.

$x < \frac{- 1 \cdot 2 + 9}{2}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$x < \frac{- 2 + 9}{2}$

Add $- 2$ and $9$ .

$x < \frac{7}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{7}{2}$

Interval Notation:

$(- \infty, \frac{7}{2})$