Solve for q 0.5(2q+1)=0.75q

$0.5 (2 q + 1) = 0.75 q$

Step 1

Simplify $0.5 (2 q + 1)$ .

Start simplifying.

$0 + 0 + 0.5 (2 q + 1) = 0.75 q$

Simplify by adding zeros.

$0.5 (2 q + 1) = 0.75 q$

Apply the distributive property.

$0.5 (2 q) + 0.5 \cdot 1 = 0.75 q$

Multiply $0.5 (2 q)$ .

Multiply $2$ by $0.5$ .

$1 q + 0.5 \cdot 1 = 0.75 q$

Multiply $q$ by $1$ .

$q + 0.5 \cdot 1 = 0.75 q$

Multiply $0.5$ by $1$ .

$q + 0.5 = 0.75 q$

Step 2

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

Subtract $0.75 q$ from both sides of the equation.

$q + 0.5 - 0.75 q = 0$

Subtract $0.75 q$ from $q$ .

$0.25 q + 0.5 = 0$

Step 3

Subtract $0.5$ from both sides of the equation.

$0.25 q = - 0.5$

Step 4

Divide each term in $0.25 q = - 0.5$ by $0.25$ and simplify.

Divide each term in $0.25 q = - 0.5$ by $0.25$ .

$\frac{0.25 q}{0.25} = \frac{- 0.5}{0.25}$

Simplify the left side.

Cancel the common factor of $0.25$ .

Cancel the common factor.

$\frac{0.25 q}{0.25} = \frac{- 0.5}{0.25}$

Divide $q$ by $1$ .

$q = \frac{- 0.5}{0.25}$

Simplify the right side.

Divide $- 0.5$ by $0.25$ .

$q = - 2$