Solve for q -5(3-q)+4=5q-11

$- 5 (3 - q) + 4 = 5 q - 11$

Step 1

Simplify $- 5 (3 - q) + 4$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot 3 - 5 (- q) + 4 = 5 q - 11$

Multiply $- 5$ by $3$ .

$- 15 - 5 (- q) + 4 = 5 q - 11$

Multiply $- 1$ by $- 5$ .

$- 15 + 5 q + 4 = 5 q - 11$

Add $- 15$ and $4$ .

$5 q - 11 = 5 q - 11$

Step 2

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

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

$5 q - 11 - 5 q = - 11$

Combine the opposite terms in $5 q - 11 - 5 q$ .

Subtract $5 q$ from $5 q$ .

$0 - 11 = - 11$

Subtract $11$ from $0$ .

$- 11 = - 11$

Step 3

Since $- 11 = - 11$ , 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:

$(- \infty, \infty)$