Solve the Inequality for x 2x-3<3x-6

$2 x - 3 < 3 x - 6$

Step 1

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

Subtract $3 x$ from both sides of the inequality.

$2 x - 3 - 3 x < - 6$

Subtract $3 x$ from $2 x$ .

$- x - 3 < - 6$

Step 2

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

Add $3$ to both sides of the inequality.

$- x < - 6 + 3$

Add $- 6$ and $3$ .

$- x < - 3$

Step 3

Divide each term in $- x < - 3$ by $- 1$ and simplify.

Divide each term in $- x < - 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x > 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 3$

Interval Notation:

$(3, \infty)$

Solve the Inequality for x 2x-3<3x-6

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