Solve for a 4(2a+2)-17<15

$4 (2 a + 2) - 17 < 15$

Step 1

Simplify $4 (2 a + 2) - 17$ .

Simplify each term.

Apply the distributive property.

$4 (2 a) + 4 \cdot 2 - 17 < 15$

Multiply $2$ by $4$ .

$8 a + 4 \cdot 2 - 17 < 15$

Multiply $4$ by $2$ .

$8 a + 8 - 17 < 15$

Subtract $17$ from $8$ .

$8 a - 9 < 15$

Step 2

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

Add $9$ to both sides of the inequality.

$8 a < 15 + 9$

Add $15$ and $9$ .

$8 a < 24$

Step 3

Divide each term in $8 a < 24$ by $8$ and simplify.

Divide each term in $8 a < 24$ by $8$ .

$\frac{8 a}{8} < \frac{24}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 a}{8} < \frac{24}{8}$

Divide $a$ by $1$ .

$a < \frac{24}{8}$

Simplify the right side.

Divide $24$ by $8$ .

$a < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a < 3$

Interval Notation:

$(- \infty, 3)$