Fill in the blanks!

Question

Expand and simplify the expression:
-5/7 (3x + 1/4y) + 9 (x/7 - 1/28y)

1. Use the distributive property to expand each expression.
(-5/7) (_) + (-5/7) (1/4y) + 9 (x/_) -9 (1/28y)

2. Combine like terms.
-15x/7 - _/28 y + 9x/7 - _/28y
-6x/7 - 14/28 y
-6x/7 - _/2 y

Answer 1

Let's fill in the blanks step by step.

1. Use the distributive property to expand each expression.

The expression to expand is: \[ -5/7 (3x + 1/4y) + 9 (x/7 - 1/28y) \]

Expanding the first part: \[ -5/7 (3x) + (-5/7)(1/4y) = -\frac{15x}{7} - \frac{5}{28}y \]

Expanding the second part: \[ 9 (x/7) - 9 (1/28y) = \frac{9x}{7} - \frac{9}{28}y \]

So we have: \[ -\frac{15x}{7} - \frac{5}{28}y + \frac{9x}{7} - \frac{9}{28}y \]

The filled-in statement is: \[ (-5/7) (3x) + (-5/7) (1/4y) + 9 (x/7) - 9 (1/28y) \]

2. Combine like terms.

Collecting like terms for \(x\): \[ -\frac{15x}{7} + \frac{9x}{7} = \frac{-15x + 9x}{7} = \frac{-6x}{7} \]

Now, for \(y\): \[ -\frac{5}{28}y - \frac{9}{28}y = \frac{-5y - 9y}{28} = \frac{-14y}{28} = -\frac{1}{2}y \]

Now putting it all together, we get: \[ -\frac{6x}{7} - \frac{1}{2}y \]

So the filled-in statements for the simplified expression are:

1. Fill-in for the first part: \((-5/7) (3x) + (-5/7) (1/4y) + 9 (x/7) - 9 (1/28y)\)
2. Fill-in for combining like terms:
   • For \(y\): \(-14\)
   • For the last term: \(-1\)

Thus: -6x/7 - 14/28 y --> -6x/7 - 1/2 y