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: $$-\frac{5}{7}(3x+\frac{1}{4}y)-9(\frac{x}{7}-\frac{1}{28}y)$$

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

$$-9\left(\frac{x}{7}\right)-9(-\frac{1}{28}y)$$ 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: $$-\frac{5}{28}y+\frac{9}{28}y=(-5+9)\frac{1}{28}y=\frac{4}{28}y=\frac{1}{7}y$$

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

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