Mass of the clothes. 2. Solve the equation 6(r+3) = (2r+12)

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1. Mass of the clothes

Identify the given masses.
The mass of the empty bag is $m$ kilograms.
The total mass of the bag when full of clothes is 16 kilograms.
Formulate the relationship between the masses.
The total mass is the sum of the mass of the empty bag and the mass of the clothes.
Total mass = Mass of empty bag + Mass of clothes
$16 = m + \text{Mass of clothes}$
Write an expression for the mass of the clothes.
To find the mass of the clothes, subtract the mass of the empty bag from the total mass.
Mass of clothes $= 16 - m$

The expression to represent the mass of the clothes is: $\boxed{(16 - m) \text{ kilograms}}$

2. Solve the equation $6(r+3) = (2r+12)$
Distribute the 6 on the left side of the equation.
$6(r+3) = 2r+12$ $6r + 6 \times 3 = 2r+12$ $6r + 18 = 2r+12$
Collect terms with $r$ on one side and constant terms on the other side.
Subtract $2r$ from both sides:
$6r - 2r + 18 = 12$ $4r + 18 = 12$
Subtract 18 from both sides:
$4r = 12 - 18$ $4r = -6$
Solve for $r$ .
Divide both sides by 4:
$r = \frac{-6}{4}$ $r = -\frac{3}{2}$
The value of $r$ is: $\boxed{-\frac{3}{2}}$

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