Question

1. solve each equation

a. $2(x - 3) = 14$

b. $-5(x - 1) = 40$

Explanation:

Part a: Solve \( 2(x - 3)=14 \)

Step 1: Divide both sides by 2

To isolate the term with \( x \), we divide both sides of the equation \( 2(x - 3)=14 \) by 2.
\( \frac{2(x - 3)}{2}=\frac{14}{2} \)
Simplifying, we get \( x - 3 = 7 \).

Step 2: Add 3 to both sides

To solve for \( x \), we add 3 to both sides of the equation \( x - 3 = 7 \).
\( x - 3 + 3 = 7 + 3 \)
Simplifying, we get \( x = 10 \).

Part b: Solve \( -5(x - 1)=45 \)

Step 1: Divide both sides by -5

To isolate the term with \( x \), we divide both sides of the equation \( -5(x - 1)=45 \) by -5.
\( \frac{-5(x - 1)}{-5}=\frac{45}{-5} \)
Simplifying, we get \( x - 1 = -9 \).

Step 2: Add 1 to both sides

To solve for \( x \), we add 1 to both sides of the equation \( x - 1 = -9 \).
\( x - 1 + 1 = -9 + 1 \)
Simplifying, we get \( x = -8 \).

Answer:

a. \( x = 10 \)
b. \( x = -8 \)