Sure! We are given the expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
To find the expression for [tex]\(PS\)[/tex], we need to add [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]. Let's perform the addition step by step:
1. Start with the given expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
2. Add the expressions together:
[tex]\[ PS = PR + RS \][/tex]
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
3. Combine the like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(4x + 3x = 7x\)[/tex]
- Combine the constant terms: [tex]\(-2 - 5 = -7\)[/tex]
4. So, the expression for [tex]\(PS\)[/tex] becomes:
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the expression that represents [tex]\(PS\)[/tex] is [tex]\(\boxed{7x - 7}\)[/tex].
