Solve the Inequality for a 21>=3(a-7)+9

$21 \geq 3 (a - 7) + 9$

Rewrite so $a$ is on the left side of the inequality.

$3 (a - 7) + 9 \leq 21$

Simplify $3 (a - 7) + 9$ .

Simplify each term.

Apply the distributive property.

$3 a + 3 \cdot - 7 + 9 \leq 21$

Multiply $3$ by $- 7$ .

$3 a - 21 + 9 \leq 21$

Add $- 21$ and $9$ .

$3 a - 12 \leq 21$

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

Add $12$ to both sides of the inequality.

$3 a \leq 21 + 12$

Add $21$ and $12$ .

$3 a \leq 33$

Divide each term in $3 a \leq 33$ by $3$ and simplify.

Divide each term in $3 a \leq 33$ by $3$ .

$\frac{3 a}{3} \leq \frac{33}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} \leq \frac{33}{3}$

Divide $a$ by $1$ .

$a \leq \frac{33}{3}$

Simplify the right side.

Divide $33$ by $3$ .

$a \leq 11$

The result can be shown in multiple forms.

Inequality Form:

$a \leq 11$

Interval Notation:

$(- \infty, 11]$