Question

6-51. solve each of the following equations for the indicated variable. show all of your steps. homework help a. $y = 2x - 5$ for $x$ b. $p = -aw + 9$ for $w$ c. $2m - 6 = 4n + 4$ for $m$ d. $bx - y = -2y$ for $y$

Explanation:

Part (a): Solve \( y = 2x - 5 \) for \( x \)

Step 1: Add 5 to both sides

To isolate the term with \( x \), we add 5 to both sides of the equation. This gives us \( y + 5 = 2x - 5 + 5 \), which simplifies to \( y + 5 = 2x \).

Step 2: Divide by 2

Now, we divide both sides of the equation by 2 to solve for \( x \). So, \( \frac{y + 5}{2}=x \), or we can write it as \( x=\frac{y + 5}{2} \).

Step 1: Subtract 9 from both sides

We want to isolate the term with \( w \), so we subtract 9 from both sides. This gives \( p - 9=-aw+9 - 9 \), which simplifies to \( p - 9=-aw \).

Step 2: Divide by \(-a\) (assuming \( a

eq0 \))
Now, we divide both sides of the equation by \(-a\) to solve for \( w \). So, \( \frac{p - 9}{-a}=w \), which can be rewritten as \( w=\frac{9 - p}{a} \) (by multiplying numerator and denominator by - 1).

Step 1: Add 6 to both sides

To isolate the term with \( m \), we add 6 to both sides. This gives \( 2m-6 + 6=4n + 4+6 \), which simplifies to \( 2m=4n + 10 \).

Step 2: Divide by 2

Now, we divide both sides of the equation by 2 to solve for \( m \). So, \( \frac{2m}{2}=\frac{4n + 10}{2} \), which simplifies to \( m = 2n+5 \).

Answer:

\( x=\frac{y + 5}{2} \)

Part (b): Solve \( p=-aw + 9 \) for \( w \)