Solve for a (2a+3)-(4a-8)=7

$(2 a + 3) - (4 a - 8) = 7$

Step 1

Simplify $2 a + 3 - (4 a - 8)$ .

Simplify each term.

Apply the distributive property.

$2 a + 3 - (4 a) - - 8 = 7$

Multiply $4$ by $- 1$ .

$2 a + 3 - 4 a - - 8 = 7$

Multiply $- 1$ by $- 8$ .

$2 a + 3 - 4 a + 8 = 7$

Simplify by adding terms.

Subtract $4 a$ from $2 a$ .

$- 2 a + 3 + 8 = 7$

Add $3$ and $8$ .

$- 2 a + 11 = 7$

Step 2

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

Subtract $11$ from both sides of the equation.

$- 2 a = 7 - 11$

Subtract $11$ from $7$ .

$- 2 a = - 4$

Step 3

Divide each term in $- 2 a = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 a = - 4$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{- 4}{- 2}$

Divide $a$ by $1$ .

$a = \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$a = 2$