Solve the Inequality for a -2(4a+4)+5a>-35

$- 2 (4 a + 4) + 5 a > - 35$

Step 1

Simplify $- 2 (4 a + 4) + 5 a$ .

Simplify each term.

Apply the distributive property.

$- 2 (4 a) - 2 \cdot 4 + 5 a > - 35$

Multiply $4$ by $- 2$ .

$- 8 a - 2 \cdot 4 + 5 a > - 35$

Multiply $- 2$ by $4$ .

$- 8 a - 8 + 5 a > - 35$

Add $- 8 a$ and $5 a$ .

$- 3 a - 8 > - 35$

Step 2

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

Add $8$ to both sides of the inequality.

$- 3 a > - 35 + 8$

Add $- 35$ and $8$ .

$- 3 a > - 27$

Step 3

Divide each term in $- 3 a > - 27$ by $- 3$ and simplify.

Divide each term in $- 3 a > - 27$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 a}{- 3} < \frac{- 27}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 a}{- 3} < \frac{- 27}{- 3}$

Divide $a$ by $1$ .

$a < \frac{- 27}{- 3}$

Simplify the right side.

Divide $- 27$ by $- 3$ .

$a < 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a < 9$

Interval Notation:

$(- \infty, 9)$

Solve the Inequality for a -2(4a+4)+5a>-35

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