Solve the Inequality for x 1+5(x-8)<=2-(x+5)

$1 + 5 (x - 8) \leq 2 - (x + 5)$

Simplify $1 + 5 (x - 8)$ .

Simplify each term.

Apply the distributive property.

$1 + 5 x + 5 \cdot - 8 \leq 2 - (x + 5)$

Multiply $5$ by $- 8$ .

$1 + 5 x - 40 \leq 2 - (x + 5)$

Subtract $40$ from $1$ .

$5 x - 39 \leq 2 - (x + 5)$

Simplify $2 - (x + 5)$ .

Simplify each term.

Apply the distributive property.

$5 x - 39 \leq 2 - x - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$5 x - 39 \leq 2 - x - 5$

Subtract $5$ from $2$ .

$5 x - 39 \leq - x - 3$

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

Add $x$ to both sides of the inequality.

$5 x - 39 + x \leq - 3$

Add $5 x$ and $x$ .

$6 x - 39 \leq - 3$

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

Add $39$ to both sides of the inequality.

$6 x \leq - 3 + 39$

Add $- 3$ and $39$ .

$6 x \leq 36$

Divide each term in $6 x \leq 36$ by $6$ and simplify.

Divide each term in $6 x \leq 36$ by $6$ .

$\frac{6 x}{6} \leq \frac{36}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} \leq \frac{36}{6}$

Divide $x$ by $1$ .

$x \leq \frac{36}{6}$

Simplify the right side.

Divide $36$ by $6$ .

$x \leq 6$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 6$

Interval Notation:

$(- \infty, 6]$