Solve for x 2x<x-4<=3x+8

$2 x < x - 4 \leq 3 x + 8$

Step 1

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

Subtract $x$ from both sides of the inequality.

$2 x - x < - 4$

Subtract $x$ from $2 x$ .

$x < - 4$

Step 2

Solve $x - 4 \leq 3 x + 8$ for $x$ .

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

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

$x - 4 - 3 x \leq 8$

Subtract $3 x$ from $x$ .

$- 2 x - 4 \leq 8$

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

Add $4$ to both sides of the inequality.

$- 2 x \leq 8 + 4$

Add $8$ and $4$ .

$- 2 x \leq 12$

Divide each term in $- 2 x \leq 12$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{12}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$x \geq - 6$

Step 3

Find the intersection of $x < - 4$ and $x \geq - 6$ .

$- 6 \leq x < - 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 6 \leq x < - 4$

Interval Notation:

$[- 6, - 4)$

Step 5

Solve for x 2x<x-4<=3x+8

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