Solve for x 2x-3>3x-1

$2 x - 3 > 3 x - 1$

Step 1

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

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

$2 x - 3 - 3 x > - 1$

Subtract $3 x$ from $2 x$ .

$- x - 3 > - 1$

Step 2

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

Add $3$ to both sides of the inequality.

$- x > - 1 + 3$

Add $- 1$ and $3$ .

$- x > 2$

Step 3

Divide each term in $- x > 2$ by $- 1$ and simplify.

Divide each term in $- x > 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $2$ by $- 1$ .

$x < - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 2$

Interval Notation:

$(- \infty, - 2)$

Solve for x 2x-3>3x-1

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