Algebra Examples

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

Step 1

Simplify $5 (a - 3)$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $5$ by $- 3$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Subtract $5 a$ from $5 a$ .

$0 - 15 \leq - 6$

Step 2.2.2

Subtract $15$ from $0$ .

$- 15 \leq - 6$

Step 3

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

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$