Solve the Inequality for a a-6<=15+8a

$a - 6 \leq 15 + 8 a$

Step 1

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

Subtract $8 a$ from both sides of the inequality.

$a - 6 - 8 a \leq 15$

Subtract $8 a$ from $a$ .

$- 7 a - 6 \leq 15$

Step 2

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

Add $6$ to both sides of the inequality.

$- 7 a \leq 15 + 6$

Add $15$ and $6$ .

$- 7 a \leq 21$

Step 3

Divide each term in $- 7 a \leq 21$ by $- 7$ and simplify.

Divide each term in $- 7 a \leq 21$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 a}{- 7} \geq \frac{21}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 a}{- 7} \geq \frac{21}{- 7}$

Divide $a$ by $1$ .

$a \geq \frac{21}{- 7}$

Simplify the right side.

Divide $21$ by $- 7$ .

$a \geq - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a \geq - 3$

Interval Notation:

$[- 3, \infty)$

Solve the Inequality for a a-6<=15+8a

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