Solve the Inequality for x x<3x+2<2x+6

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

Step 1

Solve $x < 3 x + 2$ for $x$ .

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

Subtract $3 x$ from both sides of the inequality.

$x - 3 x < 2$

Subtract $3 x$ from $x$ .

$- 2 x < 2$

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 2

Solve $3 x + 2 < 2 x + 6$ for $x$ .

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

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

$3 x + 2 - 2 x < 6$

Subtract $2 x$ from $3 x$ .

$x + 2 < 6$

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

Subtract $2$ from both sides of the inequality.

$x < 6 - 2$

Subtract $2$ from $6$ .

$x < 4$

Step 3

Find the intersection of $x > - 1$ and $x < 4$ .

$- 1 < x < 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x < 4$

Interval Notation:

$(- 1, 4)$

Step 5

Solve the Inequality for x x<3x+2<2x+6

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