Solve the Inequality for x -3x+5x-2>-4x+1

$- 3 x + 5 x - 2 > - 4 x + 1$

Step 1

Add $- 3 x$ and $5 x$ .

$2 x - 2 > - 4 x + 1$

Step 2

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

Add $4 x$ to both sides of the inequality.

$2 x - 2 + 4 x > 1$

Add $2 x$ and $4 x$ .

$6 x - 2 > 1$

Step 3

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

Add $2$ to both sides of the inequality.

$6 x > 1 + 2$

Add $1$ and $2$ .

$6 x > 3$

Step 4

Divide each term in $6 x > 3$ by $6$ and simplify.

Divide each term in $6 x > 3$ by $6$ .

$\frac{6 x}{6} > \frac{3}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} > \frac{3}{6}$

Divide $x$ by $1$ .

$x > \frac{3}{6}$

Simplify the right side.

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$x > \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$x > \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$x > \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

$x > \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{1}{2}$

Interval Notation:

$(\frac{1}{2}, \infty)$