Question

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

Explanation:

Step1: Identify the segment addition

From the number line, \( PS = PR + RS \).

Step2: Substitute the given expressions

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

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")