Solve the Inequality for x -3x+5<=4-x

$- 3 x + 5 \leq 4 - x$

Step 1

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

Add $x$ to both sides of the inequality.

$- 3 x + 5 + x \leq 4$

Add $- 3 x$ and $x$ .

$- 2 x + 5 \leq 4$

Step 2

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

Subtract $5$ from both sides of the inequality.

$- 2 x \leq 4 - 5$

Subtract $5$ from $4$ .

$- 2 x \leq - 1$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

Step 4

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

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

Solve the Inequality for x -3x+5<=4-x

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