Answer :
To determine the expression for [tex]\( PS \)[/tex], we start by noting that [tex]\( PS \)[/tex] is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].
Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
We are looking for:
[tex]\[ PS = PR + RS \][/tex]
Now, 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]
Next, we simplify this expression by combining like terms:
1. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 4x + 3x = 7x \][/tex]
2. Combine the constant terms:
[tex]\[ -2 - 5 = -7 \][/tex]
So, the simplified expression for [tex]\( PS \)[/tex] is:
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ \boxed{7x - 7} \][/tex]
Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
We are looking for:
[tex]\[ PS = PR + RS \][/tex]
Now, 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]
Next, we simplify this expression by combining like terms:
1. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 4x + 3x = 7x \][/tex]
2. Combine the constant terms:
[tex]\[ -2 - 5 = -7 \][/tex]
So, the simplified expression for [tex]\( PS \)[/tex] is:
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ \boxed{7x - 7} \][/tex]
