Solve the Inequality for x 3(x-2)-(1-x)>2x-7

$3 (x - 2) - (1 - x) > 2 x - 7$

Simplify $3 (x - 2) - (1 - x)$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 2 - (1 - x) > 2 x - 7$

Multiply $3$ by $- 2$ .

$3 x - 6 - (1 - x) > 2 x - 7$

Apply the distributive property.

$3 x - 6 - 1 \cdot 1 - - x > 2 x - 7$

Multiply $- 1$ by $1$ .

$3 x - 6 - 1 - - x > 2 x - 7$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$3 x - 6 - 1 + 1 x > 2 x - 7$

Multiply $x$ by $1$ .

$3 x - 6 - 1 + x > 2 x - 7$

Simplify by adding terms.

Add $3 x$ and $x$ .

$4 x - 6 - 1 > 2 x - 7$

Subtract $1$ from $- 6$ .

$4 x - 7 > 2 x - 7$

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

Subtract $2 x$ from both sides of the inequality.

$4 x - 7 - 2 x > - 7$

Subtract $2 x$ from $4 x$ .

$2 x - 7 > - 7$

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

Add $7$ to both sides of the inequality.

$2 x > - 7 + 7$

Add $- 7$ and $7$ .

$2 x > 0$

Divide each term in $2 x > 0$ by $2$ and simplify.

Divide each term in $2 x > 0$ by $2$ .

$\frac{2 x}{2} > \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{0}{2}$

Divide $x$ by $1$ .

$x > \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x > 0$

The result can be shown in multiple forms.

Inequality Form:

$x > 0$

Interval Notation:

$(0, \infty)$

Solve the Inequality for x 3(x-2)-(1-x)>2x-7

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