Solve for x 3x<2x+4<=6

$3 x < 2 x + 4 \leq 6$

Step 1

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

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

$3 x - 2 x < 4$

Subtract $2 x$ from $3 x$ .

$x < 4$

Step 2

Solve $2 x + 4 \leq 6$ for $x$ .

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

Subtract $4$ from both sides of the inequality.

$2 x \leq 6 - 4$

Subtract $4$ from $6$ .

$2 x \leq 2$

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

Divide each term in $2 x \leq 2$ by $2$ .

$\frac{2 x}{2} \leq \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{2}{2}$

Divide $x$ by $1$ .

$x \leq \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x \leq 1$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq 1$

Interval Notation:

$(- \infty, 1]$

Step 4