Solve the Inequality for x (-3)(2x-3)<5|7-10|

$(- 3) (2 x - 3) < 5 | 7 - 10 |$

Simplify.

Subtract $10$ from $7$ .

$- 3 (2 x - 3) < 5 | - 3 |$

The absolute value is the distance between a number and zero. The distance between $- 3$ and $0$ is $3$ .

$- 3 (2 x - 3) < 5 \cdot 3$

Multiply $5$ by $3$ .

$- 3 (2 x - 3) < 15$

Divide each term in $- 3 (2 x - 3) < 15$ by $- 3$ and simplify.

Divide each term in $- 3 (2 x - 3) < 15$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 (2 x - 3)}{- 3} > \frac{15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 (2 x - 3)}{- 3} > \frac{15}{- 3}$

Divide $2 x - 3$ by $1$ .

$2 x - 3 > \frac{15}{- 3}$

Simplify the right side.

Divide $15$ by $- 3$ .

$2 x - 3 > - 5$

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

Add $3$ to both sides of the inequality.

$2 x > - 5 + 3$

Add $- 5$ and $3$ .

$2 x > - 2$

Divide each term in $2 x > - 2$ by $2$ and simplify.

Divide each term in $2 x > - 2$ by $2$ .

$\frac{2 x}{2} > \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 2}{2}$

Divide $x$ by $1$ .

$x > \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$x > - 1$

The result can be shown in multiple forms.

Inequality Form:

$x > - 1$

Interval Notation:

$(- 1, \infty)$

Solve the Inequality for x (-3)(2x-3)<5|7-10|

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