Solve the Inequality for x 2x-(3-x)>x+1

$2 x - (3 - x) > x + 1$

Step 1

Simplify $2 x - (3 - x)$ .

Simplify each term.

Apply the distributive property.

$2 x - 1 \cdot 3 - - x > x + 1$

Multiply $- 1$ by $3$ .

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

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Add $2 x$ and $x$ .

$3 x - 3 > x + 1$

Step 2

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

Subtract $x$ from both sides of the inequality.

$3 x - 3 - x > 1$

Subtract $x$ from $3 x$ .

$2 x - 3 > 1$

Step 3

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

Add $3$ to both sides of the inequality.

$2 x > 1 + 3$

Add $1$ and $3$ .

$2 x > 4$

Step 4

Divide each term in $2 x > 4$ by $2$ and simplify.

Divide each term in $2 x > 4$ by $2$ .

$\frac{2 x}{2} > \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{4}{2}$

Divide $x$ by $1$ .

$x > \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x > 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$

Solve the Inequality for x 2x-(3-x)>x+1

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