Solve the Inequality for x 2(x+1)-3(x-2)<x+6

$2 (x + 1) - 3 (x - 2) < x + 6$

Step 1

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

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot 1 - 3 (x - 2) < x + 6$

Multiply $2$ by $1$ .

$2 x + 2 - 3 (x - 2) < x + 6$

Apply the distributive property.

$2 x + 2 - 3 x - 3 \cdot - 2 < x + 6$

Multiply $- 3$ by $- 2$ .

$2 x + 2 - 3 x + 6 < x + 6$

Simplify by adding terms.

Subtract $3 x$ from $2 x$ .

$- x + 2 + 6 < x + 6$

Add $2$ and $6$ .

$- x + 8 < x + 6$

Step 2

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

Subtract $x$ from both sides of the inequality.

$- x + 8 - x < 6$

Subtract $x$ from $- x$ .

$- 2 x + 8 < 6$

Step 3

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

Subtract $8$ from both sides of the inequality.

$- 2 x < 6 - 8$

Subtract $8$ from $6$ .

$- 2 x < - 2$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x > 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 1$

Interval Notation:

$(1, \infty)$

Solve the Inequality for x 2(x+1)-3(x-2)<x+6

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