Solve for x 3(x-5)<=x-8

$3 (x - 5) \leq x - 8$

Simplify $3 (x - 5)$ .

Rewrite.

$0 + 0 + 3 (x - 5) \leq x - 8$

Simplify by adding zeros.

$3 (x - 5) \leq x - 8$

Apply the distributive property.

$3 x + 3 \cdot - 5 \leq x - 8$

Multiply $3$ by $- 5$ .

$3 x - 15 \leq x - 8$

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

Subtract $x$ from both sides of the inequality.

$3 x - 15 - x \leq - 8$

Subtract $x$ from $3 x$ .

$2 x - 15 \leq - 8$

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

Add $15$ to both sides of the inequality.

$2 x \leq - 8 + 15$

Add $- 8$ and $15$ .

$2 x \leq 7$

Divide each term in $2 x \leq 7$ by $2$ and simplify.

Divide each term in $2 x \leq 7$ by $2$ .

$\frac{2 x}{2} \leq \frac{7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{7}{2}$

Divide $x$ by $1$ .

$x \leq \frac{7}{2}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{7}{2}$

Interval Notation:

$(- \infty, \frac{7}{2}]$