Solve for a 2<2a-3(1-a)<10

$2 < 2 a - 3 (1 - a) < 10$

Step 1

Simplify each term.

Apply the distributive property.

$2 < 2 a - 3 \cdot 1 - 3 (- a) < 10$

Multiply $- 3$ by $1$ .

$2 < 2 a - 3 - 3 (- a) < 10$

Multiply $- 1$ by $- 3$ .

$2 < 2 a - 3 + 3 a < 10$

Step 2

Add $2 a$ and $3 a$ .

$2 < 5 a - 3 < 10$

Step 3

Move all terms not containing $a$ from the center section of the inequality.

Add $3$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$2 + 3 < 5 a < 10 + 3$

Add $2$ and $3$ .

$5 < 5 a < 10 + 3$

Add $10$ and $3$ .

$5 < 5 a < 13$

Step 4

Divide each term in the inequality by $5$ .

$\frac{5}{5} < \frac{5 a}{5} < \frac{13}{5}$

Step 5

Divide $5$ by $5$ .

$1 < \frac{5 a}{5} < \frac{13}{5}$

Step 6

Cancel the common factor of $5$ .

Cancel the common factor.

$1 < \frac{5 a}{5} < \frac{13}{5}$

Divide $a$ by $1$ .

$1 < a < \frac{13}{5}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$1 < a < \frac{13}{5}$

Interval Notation:

$(1, \frac{13}{5})$

Step 8