Question

if pr = 4x - 2 and rs = 3x - 5, which expression represents ps?
p q r s
o x-7
o x-3
o 7x-7
o 7x+3

Explanation:

Step1: Analyze the segment addition

From the number line, \( PS = PR + RS \) because \( R \) is between \( P \) and \( S \).

Step2: Substitute the given expressions

We know \( PR = 4x - 2 \) and \( RS = 3x - 5 \). So substitute these into the equation for \( PS \):
\( PS=(4x - 2)+(3x - 5) \)

Step3: Combine like terms

Combine the \( x \)-terms and the constant terms:
\( 4x+3x=7x \) and \( - 2-5=-7 \)
So \( PS = 7x-7 \)

Answer:

\( 7x - 7 \) (corresponding to the option "7x−7")