Solve the Inequality for a 5(a-3)<=5a-6

$5 (a - 3) \leq 5 a - 6$

Simplify $5 (a - 3)$ .

Rewrite.

$0 + 0 + 5 (a - 3) \leq 5 a - 6$

Simplify by adding zeros.

$5 (a - 3) \leq 5 a - 6$

Apply the distributive property.

$5 a + 5 \cdot - 3 \leq 5 a - 6$

Multiply $5$ by $- 3$ .

$5 a - 15 \leq 5 a - 6$

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

Subtract $5 a$ from both sides of the inequality.

$5 a - 15 - 5 a \leq - 6$

Combine the opposite terms in $5 a - 15 - 5 a$ .

Subtract $5 a$ from $5 a$ .

$0 - 15 \leq - 6$

Subtract $15$ from $0$ .

$- 15 \leq - 6$

Since $- 15 \leq - 6$ , the inequality will always be true.

Always true

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$