Question

1. solve the following equations:

a) ( p + 35 = 46 )
b) ( r - 29 = 2 )
c) ( x + 3 = 5 )
d) ( 8m = 32 )
e) ( 5y = 35 )
f) ( -2x = 18 )
g) ( 3x + 2y = 64 )
h) ( \frac{4}{13} = \frac{8}{65} )
i) ( \frac{4}{15} = \frac{8}{15} )

Explanation:

Looking at the image, there are several equations to solve. Let's pick one, say \( p + 35 = 46 \) (from the top left, maybe? The handwriting is a bit unclear, but let's assume a simple linear equation like \( p + 35 = 46 \)).

Step 1: Isolate the variable \( p \)

To solve for \( p \), we subtract 35 from both sides of the equation. The equation is \( p + 35 = 46 \). Subtracting 35 from both sides gives \( p + 35 - 35 = 46 - 35 \).

Step 2: Simplify both sides

Simplifying the left side: \( p + 0 = p \). Simplifying the right side: \( 46 - 35 = 11 \). So \( p = 11 \).

Step 1: Isolate \( m \)

Divide both sides by 8. The equation is \( 8m = 32 \), so \( \frac{8m}{8} = \frac{32}{8} \).

Step 2: Simplify

Left side: \( m \), right side: \( 4 \). So \( m = 4 \).

Step 1: Divide both sides by 8

Given \( 8m = 32 \), divide each side by 8: \( \frac{8m}{8} = \frac{32}{8} \)

Step 2: Simplify

\( m = 4 \)

Answer:

\( p = 11 \)

(If we take another equation, like \( 8m = 32 \) (middle left):