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

Question

(-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 work through the expansion and simplification of the expression step by step.

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

We'll expand each term separately.

Step 1: Expand the first term

\[ -\frac{5}{7}(3x) - \frac{5}{7}\left(\frac{1}{4}y\right) \] Calculating these:

1. \(-\frac{5}{7} \cdot 3x = -\frac{15}{7}x\)
2. \(-\frac{5}{7} \cdot \frac{1}{4}y = -\frac{5}{28}y\)

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

Step 2: Expand the second term

\[ -9\left(\frac{x}{7}\right) - 9\left(-\frac{1}{28}y\right) \] Calculating these:

1. \(-9 \cdot \frac{x}{7} = -\frac{9}{7}x\)
2. \(-9 \cdot -\frac{1}{28}y = \frac{9}{28}y\)

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

Step 3: Combine the results

Now we will combine the results from both expansions: \[ -\frac{15}{7}x - \frac{5}{28}y - \frac{9}{7}x + \frac{9}{28}y \]

Step 4: Combine the \(x\) terms and the \(y\) terms

• For the \(x\) terms: \[ -\frac{15}{7}x - \frac{9}{7}x = -\left(\frac{15 + 9}{7}\right)x = -\frac{24}{7}x \]

• For the \(y\) terms: \[ -\frac{5}{28}y + \frac{9}{28}y = \left(-5 + 9\right)\frac{1}{28}y = \frac{4}{28}y = \frac{1}{7}y \]

Thus, putting it all together, we have: \[ -\frac{24}{7}x + \frac{1}{7}y \]

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