Answer :
To find the expression representing [tex]\( PS \)[/tex], we need to understand that [tex]\( PS \)[/tex] would be the sum of the segments [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]. Here are the step-by-step calculations:
1. We are given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
2. Since [tex]\( PS \)[/tex] is the total length consisting of both [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
3. Substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] into the equation for [tex]\( PS \)[/tex]:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
4. Combine the like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]
5. Simplify the expression by adding the coefficients of [tex]\( x \)[/tex] and the constant terms:
[tex]\[ PS = 7x - 7 \][/tex]
After following these steps, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
So, the correct choice is:
[tex]\[ \boxed{7x - 7} \][/tex]
1. We are given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
2. Since [tex]\( PS \)[/tex] is the total length consisting of both [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
3. Substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] into the equation for [tex]\( PS \)[/tex]:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
4. Combine the like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]
5. Simplify the expression by adding the coefficients of [tex]\( x \)[/tex] and the constant terms:
[tex]\[ PS = 7x - 7 \][/tex]
After following these steps, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
So, the correct choice is:
[tex]\[ \boxed{7x - 7} \][/tex]
