Solve for a 7a-2b=5a+b

$7 a - 2 b = 5 a + b$

Step 1

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

Subtract $5 a$ from both sides of the equation.

$7 a - 2 b - 5 a = b$

Subtract $5 a$ from $7 a$ .

$2 a - 2 b = b$

Step 2

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

Add $2 b$ to both sides of the equation.

$2 a = b + 2 b$

Add $b$ and $2 b$ .

$2 a = 3 b$

Step 3

Divide each term in $2 a = 3 b$ by $2$ and simplify.

Divide each term in $2 a = 3 b$ by $2$ .

$\frac{2 a}{2} = \frac{3 b}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} = \frac{3 b}{2}$

Divide $a$ by $1$ .

$a = \frac{3 b}{2}$