Question

a. 3x + 2 = y, for x
b. 4xyz = m, for y
c. 2(m + 3) = n, for m
d. 3t + 2 + 5t = z, for t

Explanation:

Part c: Solve \( 2(m + 3)=n \) for \( m \)

Step 1: Divide both sides by 2

To isolate the term with \( m \), we divide both sides of the equation \( 2(m + 3)=n \) by 2.
\( \frac{2(m + 3)}{2}=\frac{n}{2} \)
Simplifying the left side, we get \( m + 3=\frac{n}{2} \)

Step 2: Subtract 3 from both sides

To solve for \( m \), we subtract 3 from both sides of the equation \( m + 3=\frac{n}{2} \).
\( m + 3-3=\frac{n}{2}-3 \)
Simplifying the left side, we get \( m=\frac{n}{2}-3 \) or we can write it as \( m=\frac{n - 6}{2} \)

Part d: Solve \( 3t + 2+5t=z \) for \( t \)

Step 1: Combine like terms

First, we combine the terms with \( t \) on the left side of the equation \( 3t + 2+5t=z \).
\( (3t + 5t)+2=z \)
\( 8t+2 = z \)

Step 2: Subtract 2 from both sides

Subtract 2 from both sides of the equation \( 8t + 2=z \) to isolate the term with \( t \).
\( 8t+2 - 2=z - 2 \)
Simplifying the left side, we get \( 8t=z - 2 \)

Step 3: Divide both sides by 8

Divide both sides of the equation \( 8t=z - 2 \) by 8 to solve for \( t \).
\( \frac{8t}{8}=\frac{z - 2}{8} \)
Simplifying the left side, we get \( t=\frac{z - 2}{8} \)

Answer:

s:

• For part c: \( \boldsymbol{m=\frac{n}{2}-3} \) (or \( \boldsymbol{m=\frac{n - 6}{2}} \))
• For part d: \( \boldsymbol{t=\frac{z - 2}{8}} \)