Solve for q 14-(2q+5)=-2q+9

$14 - (2 q + 5) = - 2 q + 9$

Step 1

Simplify $14 - (2 q + 5)$ .

Simplify each term.

Apply the distributive property.

$14 - (2 q) - 1 \cdot 5 = - 2 q + 9$

Multiply $2$ by $- 1$ .

$14 - 2 q - 1 \cdot 5 = - 2 q + 9$

Multiply $- 1$ by $5$ .

$14 - 2 q - 5 = - 2 q + 9$

Subtract $5$ from $14$ .

$- 2 q + 9 = - 2 q + 9$

Step 2

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

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

$- 2 q + 9 + 2 q = 9$

Combine the opposite terms in $- 2 q + 9 + 2 q$ .

Add $- 2 q$ and $2 q$ .

$0 + 9 = 9$

Add $0$ and $9$ .

$9 = 9$

Step 3

Since $9 = 9$ , the equation will always be true for any value of $q$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$