Solve the Inequality for x 2+3x<=8-x

$2 + 3 x \leq 8 - x$

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

Add $x$ to both sides of the inequality.

$2 + 3 x + x \leq 8$

Add $3 x$ and $x$ .

$2 + 4 x \leq 8$

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

Subtract $2$ from both sides of the inequality.

$4 x \leq 8 - 2$

Subtract $2$ from $8$ .

$4 x \leq 6$

Divide each term in $4 x \leq 6$ by $4$ and simplify.

Divide each term in $4 x \leq 6$ by $4$ .

$\frac{4 x}{4} \leq \frac{6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \leq \frac{6}{4}$

Divide $x$ by $1$ .

$x \leq \frac{6}{4}$

Simplify the right side.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$x \leq \frac{2 (3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x \leq \frac{2 \cdot 3}{2 \cdot 2}$

Cancel the common factor.

$x \leq \frac{2 \cdot 3}{2 \cdot 2}$

Rewrite the expression.

$x \leq \frac{3}{2}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{3}{2}$

Interval Notation:

$(- \infty, \frac{3}{2}]$