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

Question

Fill in the blanks
(-5/7)(3x/1) + (-5/7)(1/4 ?) + (-9)(x/?) + (-9)(-1/28y)
-15x/7 - 5/28y - 9x/7 + ?/28y
-?/7x + 4/28y
-24/7x + ?/7y

Answer 1

Let's expand and simplify the expression step by step:

The original expression given is: \[ -\frac{5}{7}(3x + \frac{1}{4}y) - 9\left(\frac{x}{7} - \frac{1}{28}y\right) \]

Step 1: Expand the first part \[ -\frac{5}{7}(3x) - \frac{5}{7}\left(\frac{1}{4}y\right) = -\frac{15}{7}x - \frac{5}{28}y \]

Step 2: Expand the second part \[ -9\left(\frac{x}{7}\right) + 9\left(\frac{1}{28}y\right) = -\frac{9}{7}x + \frac{9}{28}y \]

Step 3: Combine both parts Now, combine the two parts: \[ -\frac{15}{7}x - \frac{5}{28}y - \frac{9}{7}x + \frac{9}{28}y \]

Step 4: Combine like terms For the \(x\) terms: \[ -\frac{15}{7}x - \frac{9}{7}x = -\frac{24}{7}x \]

For the \(y\) terms: \[ -\frac{5}{28}y + \frac{9}{28}y = \frac{4}{28}y \]

Step 5: Putting it all together Thus, we have: \[ -\frac{24}{7}x + \frac{4}{28}y \]

Step 6: Simplify \(\frac{4}{28}\) to \(\frac{1}{7}\) \[ \frac{4}{28}y = \frac{1}{7}y \]

So, the final simplified expression is: \[ -\frac{24}{7}x + \frac{1}{7}y \]

Now, let's fill out the blanks:

• Expanding: \((-5/7)(3x/1) + (-5/7)(1/4y) + (-9)(x/7) + (-9)(-1/28y)\)

• We fill in: (-5/7)(3x/1) + (-5/7)(1/4y) + (-9)(x/7) + (-9)(-1/28y)

  Which will lead to: \[

• \frac{15}{7} x - \frac{5}{28} y - \frac{9}{7} x + \frac{9}{28} y \]

• Combining terms for \(x\): \(-\frac{15}{7} - \frac{9}{7} = -\frac{24}{7} x\)

• Combining terms for \(y\): \(-\frac{5}{28} + \frac{9}{28} = \frac{4}{28} = \frac{1}{7}y\)

Therefore, the final expression in the form stated is: \[ -\frac{24}{7}x + \frac{1}{7}y \]

So, to fill in the final blanks:

• The values are:

1. -24 for the first blank,
2. 4 for the second blank,
3. 1 for the third blank.