Convert to Set Notation 12a-15>=3a-6

$12 a - 15 \geq 3 a - 6$

Step 1

Solve $a \geq 1$ .

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

Subtract $3 a$ from both sides of the inequality.

$12 a - 15 - 3 a \geq - 6$

Subtract $3 a$ from $12 a$ .

$9 a - 15 \geq - 6$

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

Add $15$ to both sides of the inequality.

$9 a \geq - 6 + 15$

Add $- 6$ and $15$ .

$9 a \geq 9$

Divide each term in $9 a \geq 9$ by $9$ and simplify.

Divide each term in $9 a \geq 9$ by $9$ .

$\frac{9 a}{9} \geq \frac{9}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 a}{9} \geq \frac{9}{9}$

Divide $a$ by $1$ .

$a \geq \frac{9}{9}$

Simplify the right side.

Divide $9$ by $9$ .

$a \geq 1$

Step 2

Use the inequality $a \geq 1$ to build the set notation.

${a | a \geq 1}$

Step 3